Some colleges don't accept transfer students, others do .... it's not a policy of the coaching staff usually, it a College/University policy, and the one's that don't, public and private are the exception, not the rule.
Here's the skinny from the NCAA's policies and guidelines on the rules for competition on transfer students. The sections on "Qualifier" and "Not a Qualifier" is determined by their status coming out of HS, based on their Core GPA and SAT scores.
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14.5.4 Two-Year College Transfers
A student who transfers to a member institution from a two-year college or from a branch school that conducts an intercollegiate athletics program must complete an academic year of residence unless the student meets the following eligibility requirements applicable to the division of which the certifying institution is a member. Further, a transfer student-athlete admitted after the 12th class day may not utilize that semester or quarter for the purpose of establishing residency. (Revised: 1/10/92)
14.5.4.1 Qualifier
A transfer student from a two-year college who was a qualifier (per Bylaw 14.3.1.1) is eligible for competition in Division I institutions the first academic year in residence only if the student has spent at least one full-time semester or one full-time quarter in residence at the two-year college (excluding summer sessions), presented a minimum grade-point average of 2.000 (see Bylaw 14.5.4.5.3.2) and satisfactorily completed an average of at least 12-semester or -quarter hours of transferable-degree credit acceptable toward any baccalaureate degree program at the certifying institution for each full-time academic term of attendance at the two-year college. (Revised: 4/24/03 effective 8/1/03; for those students entering an NCAA institution on a full-time basis on or after 8/1/03)
14.5.4.2 Not a Qualifier
A transfer student from a two-year college who was not a qualifier (per Bylaw 14.3.1.1) is eligible for institutional financial aid, practice and competition the first academic year in residence only if the student has graduated from the two-year college, has completed satisfactorily a minimum of 48-semester or 72-quarter hours of transferable-degree credit acceptable toward any baccalaureate degree program at the certifying institution and has attended a two-year college as a full-time student for at least three semesters or four quarters (excluding summer terms). In addition, such a student must have a cumulative grade-point average of 2.000 (see Bylaw 14.5.4.5.3.2). (Revised: 1/10/90 effective 8/1/90, 1/9/96 effective 8/1/96 for those student-athletes first entering a two-year collegiate institution on or after 8/1/96; 4/24/03 effective 8/1/03 for those students first entering an NCAA institution on a full-time basis on or after 8/1/03; 6/1/06)
14.5.4.3 Status as Qualifier or Nonqualifier
A prospective student-athlete who does not graduate from high school before enrolling as a regular student in a two-year college may not transfer work back to the high school, graduate from the high school and establish initial eligibility at a member institution on the basis of the revised high school record. Such a student is considered to be a two-year college transfer who was a nonqualifier.
14.5.4.5 Two-Year College Transfer Regulations
The following regulations shall be applied in administering the eligibility requirements for two-year college transfers.
14.5.4.5.1 Multiple Two-Year Colleges
When a student-athlete has been in residence at two or more two-year colleges, the terms of residence at all two-year colleges may be combined in order to satisfy the residence requirement. All grades and all course credits that are transferable from the two-year colleges to the member institution shall be considered in determining the student-athlete's eligibility under Bylaw 14.5 (see also Bylaw 14.5.6). In addition, at least 25 percent of the credit hours used to fulfill the student’s academic degree requirements must be earned at the two-year college that awards the degree per Bylaw 14.5. (Revised: 1/11/94)
14.5.4.5.2 Credit Earned at Four-Year Institution
If a student-athlete attends a two-year college and, prior to regular enrollment at a member institution, attains additional credits as a part-time student in a four-year collegiate institution, the hours accumulated at the four-year institution may be utilized by the member institution in determining the student-athlete's eligibility under the two-year college transfer provisions, provided:
(a) These hours are accepted by the two-year college and are placed on the transcript or other official document by the two-year college from which the student-athlete transfers prior to the date of initial regular enrollment at the NCAA member institution; and
(b) Any official document (other than the student's transcript) utilized by the two-year college for this purpose includes the official seal of the two-year college, is signed by the appropriate academic official of the two-year college and is forwarded directly from the two-year college to the appropriate admissions official of the certifying institution.
14.5.4.5.3 Determination of Transferable Degree Credit
For the purpose of determining transferable degree credit, the institution may count those courses accepted as degree credit in any of its colleges, schools or departments.
14.5.4.5.3.1 Transferable Credit, Unacceptable Grade
Credit hours for courses with grades not considered acceptable for transferable degree credit for all students at an institution shall not be counted in determining whether the transfer requirement for total number of hours is satisfied.
14.5.4.5.3.2 Calculation of Grade-Point Average for Transferable Credit
Grades earned in all courses that are normally transferable to an institution shall be considered in determining the qualitative grade-point average for meeting transfer requirements, regardless of the grade earned or whether such grade makes the course unacceptable for transferable degree credit. Only the last grade earned in a course that has been repeated shall be included in the grade-point-average calculation.
14.5.4.5.4 Degree Requirement
In order to satisfy the two-year-college graduation requirement for eligibility immediately upon transfer from a two-year college to a member institution, a student-athlete must receive an associate or equivalent degree in an academic or technical, rather than a vocational, curriculum. The Academics/Eligibility/Compliance Cabinet shall have the authority to determine whether a two-year college degree is academic or technical, rather than vocational, in nature. (Revised: 1/10/95, 1/12/99 effective 8/1/99)
14.5.4.5.5 Transfer to Four-Year College Prior to Completion of Requirements
The requirements set forth in Bylaw 14.5.4 must be met prior to a student-athlete's transfer to the certifying institution. Thus, if a two-year college student transfers (as defined in Bylaw 14.5.2) to a member institution prior to the completion of applicable transfer requirements, the student is subject to the one-year residence requirement at the certifying institution, even though the student transfers back to the two-year college and completes the necessary requirements.
14.5.4.5.6.1 Temporary Certification, Recruited Two-Year College Transfer
If a recruited two-year college transfer reports for athletics participation before the student's high school or two-year college academic record has been certified, the student may practice, but not compete, for a maximum of 14 days. After this 14-day period, the student shall have established minimum requirements as a transfer to continue practicing or to compete. (Adopted: 1/10/90, Revised: 10/7/05)
14.5.4.5.6.1 Temporary Certification, Recruited Two-Year College Transfer
14.5.4.5.6.2 Temporary Certification, Nonrecruited Two-Year College Transfer
If a nonrecruited two-year college transfer reports for athletics participation before the student's high school or two-year college academic record has been certified, the student may practice, but not compete, for a maximum of 45 days. After this period, the student shall have established minimum requirements as a transfer to continue practicing or to compete. (Adopted: 1/10/90)
14.5.4.5.7 Competition in Year of Transfer.
A transfer student from a two-year institution, who has met the two-year transfer eligibility requirements per Bylaw 14.5.4, is not eligible to compete at the certifying institution during the segment that concludes with the NCAA championship if the student-athlete has competed at the two-year college during that segment of the same academic year in that sport. (Revised: 1/11/94, 4/29/04 effective 8/1/04)
14.5.4.6 Exceptions or Waivers for Transfer from Two-Year Colleges
A transfer student from a two-year college or from a branch school that conducts an intercollegiate athletics program is not subject to the residence requirement at the certifying institution if any one of the following conditions is met. An individual who is not a qualifier shall not be permitted to use the exceptions under this bylaw. (Revised: 4/27/06)