Separation of Church and State

I am confused as to how people can argue against US tax dollars from going to religions. The first act of Congress and the President was to establish the pay of Chaplins whom must be ordained priests. Therefore your tax money has gone to pay for religion ever since the beginning.

I understand that the US Government cannot establish a religion but establishment is an entirely different thing than paying for religion.

This is to say that I think separation of church and state is hypocritical because the US Government pays ordained priests...bottom line.