executive orders only impact those employed under the executive branch.
if you don’t like the orders... leave
I’d also suggest leaving at the most in opportune time
No, “federal contractors” does not affect only those “employed under the executive branch.” That has nothing to do with it. “Federal contractor” is such a broad category now that they don’t really have to be working for anything even remotely related to the government, but simply something contracted through some program that receives some trivial sum from the US government.
The Church doesn’t do a lot of these programs now, mostly because the abortion and gay lobby drove it out of adoption services and other related things a few years ago. About the only thing the Church gets from the Feds is what all non-profits get, a tax break.
But even if you don’t take any money, “federal contractor” restrictions are carried on to the local governments and even the private sector immediately because nobody wants to accidentally run afoul of the US government. This has a much wider reach than many people understand.