Whether they receive monies from the state or not is irrelevant.
What is relevant is that the line is run under a franchise agreement and, according to the MTA, gender segregation on the line is a direct violation of that agreement.
A private bus has a constitutional right to adhere to their religious leaders religious beliefs.
A bus has no constitutional rights whatsoever.
The operators of a bus line, on the other hand, do NOT have the “constitutional right” to put their religious beliefs ahead of their contractual agreements. Example: if you go to Dunkin’ Donuts and want to open a franchise, you will have to sign a franchise agreement with them. One feature of their franchise agreement is that the store must be open seven days a week. You cannot sign the agreement and then claim your right to close for Shabbos and not be in violation of the contract because of your “constitutional rights” to your religious beliefs.
The bus case here is no different. It doesn’t matter if you have a religious belief that transportation must be gender-segregated*. If the bus company signed a franchise/licensing agreement that such acts are in violation of the contract, then they are in violation, their religious beliefs notwithstanding.
The Wolf
* Of course, we all know that gender-segregated transportation is NOT required l’halacha. Thousands of frum people take the subway every day and no one considers them sinners for doing so.
The Wolf