Clergy performing religious duties for religious institutions would still be allowed to choose who they could perform marriage ceremonies for. But if they rented out their facilities for events like wedding receptions then they would probably have to rent them out for any couple who could pony up the fee.
Religious schools would no longer be permitted to discriminate against same sex married couples when hiring, firing, granting housing, offering benefits, and selecting admissions.
It is possible as well that any materials used in teaching or in publicizing the mission of the school could not be discriminatory against same sex marriage but would have to be neutral.
Of course they can. In fact, religious schools that do this sort of thing actually stand up better under legal scrutiny as a truly religious institution. It's the half-@ssed frauds like Catholic Charities who would be out of luck here ... because they call themselves a "religious organization" even though they have no religious qualifications for their leadership positions, do not focus their activities on religious instruction or proselytization in any way, and (consequently) get more than 60% of their funding from the government.