Just because all kinds of sinful stuff may happen around religious players doesn't necessarily mean they agree with it or accept it.
Similarly, there may be religions other than what you recognize at large in the NFL. For example a player may have a "live and let live" ethos, and not feel particularly drawn to whatever his "religious" teammates would like him to participate in. Others may be deeply religious, and still understand how and why various parts of the bible came to be -- and so do not find 3,000-year-old prohibitions against homosexuality to be the core message.
How many NFL players do what Jesus says they should do "if you would be perfect," and give away everything they physically owned to follow Jesus? Not many? Are your "religious" players offended by this behavior?
These very selectively "religious" players you talk about are bigots.
That is okay. Their interpretation of their religion says they should be bigots.
However, they'll have to keep that to themselves. It may be uncomfortable for them to have an openly gay teammate. It will very likely be more uncomfortable for the first openly gay man to play in the NFL.
I am sure some had problems playing alongside Jackie Robinson in baseball -- and yes, people were still peddling segregation as biblically derived at the time. Since the inferiority of Blacks was biblical, the logic went, so was segregation.
We're in exactly the same place. Civil rights, pure and simple. Treat people the same.
Or, has Hillel put it before the derivative version, "Do not do unto your neighbor what is hateful unto you."
If there were some scifi scenario where everybody was gay except you, and you were particularly skilled at a sport, would you want to be disqualified at the pro level because your sexuality offended the delicate sensibilities of somebody's interpretation of a religion?
Civil rights, chief. Not religion. Civil rights.