Really, the government shouldn't be in the business of recognizing religions at all.
Likewise, if a state relies on a religion for its legitimacy, then the religion chooses who is valid to serve in government and governs the practice of those outside it's congregation.
The church should be a refuge from the state, not necessarily in opposition, but in a protective sense. It should provide a way to live, but not be the only way to live. If needs be, then the state should be a refuge from the church.
As for these dogmas, if they exist, it's that they allow the things you speak of to exist and provide a framework for those things to be safely practiced. None of those things are crimes when practiced within a framework of law, but instead are the choices of free individuals and should always remain so. They are not religious functions, but secular ones. Render unto Caesar that which is Caesar's; even Jesus was OK with that.
Your mistake is equating the belief they should exist with hatred - I they should be allowed to exist for all and any restrictions in their use or practice by an individual should be governed by that that individual's conscience.
Per my religion, God gave us Free Will. The State doesn't get to take that away.
I am pretty sure secular policies would be avoiding advocating or prohibiting for atheism just as it would for any other form of views that fall into religious or faith beliefs.
The state supports, say, history teaching so religious artefacts should be partly financed by the state.
Which ones is the question.
Note: I am French, profoundly atheist and actively anti religion. But I love yhe culture and thus the history of my country.
From what I understand it usually works better to pay for results rather than effort.
"Success" is often neither quantifiable nor immediately obvious.
So, how to achieve good results, if they are needed upfront to get subsidies and subsidies are needed to offer opportunities to achieve results?
It's not always better to pay for results. Paying for effort would also allow the headcount and university size to be regulated by the market. If you are a university no one wants to adhere to, then you also would not get any subsidies and have an incentive to become better in whatever you teach, without questioning first, where to get the money from.
I see it as a try to remove people without money from education. That fits with all the wisdom trump is producing every single day. Stupid.
Universities are pretty much always basically regional-monopolies, while it's true that not every university gets the same amount of applicants, I don't think they're struggling to get students altogether? But I'm not American, so maybe it's different in the USA?
If it's not different in the US, then this kind of subsidy is much worse then the result based one, because their incentive ends at getting people into courses, not successfully finishing them. So from a profit incentive, keeping them an extra year is highly desirable