Except they weren't closing down because they were forced to, they were closing down because they couldn't get federal funding. So yes they wanted federal funding. They could have continued without federal funding.
a) Separate, unequal black schools are better than no schools at all. Over in the private sector, poorly-funded startups have to compete against big-money behemoths all the time. Which leads to...
b) That is not private sector, though. Public schools are taxpayer-funded. Black people and white people both pay into the system, and thus black people are entitled to equal treatment. But the Catholics are working entirely out of their own charity. NO ONE is entitled to ANYTHING.
P.S. I should probably add: C) the Bible condemns homosexuality. It does not condemn people for being black. These are Catholic institutions, and that's what they believe.