Only if you believe that a letter of recommendation is an entitlement, sort of like a social promotion.
Again, I return to the Supreme Court decision in Thomas v. Review Board (emphasis mine):
A person may not be compelled to choose between the exercise of a First Amendment right and participation in an otherwise available public program. It is true that the Indiana law does not compel a violation of conscience, but where the state conditions receipt of an important benefit upon conduct proscribed by a religious faith, or where it denies such a benefit because of conduct mandated by religious belief, thereby putting substantial pressure on an adherent to modify his behavior and to violate his beliefs, a burden upon religion exists. While the compulsion may be indirect, the infringement upon free exercise is nonetheless substantial
The student may be denied medical school, which is probably publicly funded to some degree, for lack of a letter of recommendation which he can only receive from this professor by violating his beliefs.
To use the racial analogy again, a black kid decades ago could have gone to a black school or he could have found a professor that didn't hate blacks to get into a public school. But those facts did not in any way justify or excuse a professor for refusing him on the basis of his race.
Likewise, a professor cannot compel, even indirectly, a student to change his religious beliefs.
As has been mentioned countless times above: 1) the student wasn't going to get a letter of recommendation from the professor anyway, as he did not take the professor's course; and 2) there is, presumably, more than one professor of the biological sciences at Texas Tech, and aspiring medical students must (one hopes) take more than one class in this field, leaving a plethora of professors from which to choose.
The law does not deal with whay may be, it deals with what is. At this moment, the student has no colorable cause of action.