"the free exercise thereof"

This is a key phrase. I have the freedom to exercise my religion. If I choose to pray, great. If my religion requires I get out a rug and face certain direction, good on me. The government cannot prevent me from exercising my religion. If I want to put out a nativity scene, that's my business and you have the right to be offended, but not to stop me.

Now a question:

If my religion requires that I proselytize (attempt to convert others) can the government stop me?

Let's test it against the first amendment. Is the government establishing a religion if I proselytize? No.

Am I freely exercising my religion if I proselytize? Yes.

Okay, so, your rights are protected (the right not to have the government require you to join my religion) and my rights are protected (the right to exercise my religion by proselytizing).

So, no, the government cannot stop me. Sure proselytizing can be annoying and rude. It might offend me. But, I can't tell the government to stop the proselytizer. I have to excerise my freedom of speech (we'll get to this later) and tell the proselytizer to go hang. The proselytizer can be forced to leave my property (protecting my property rights), but in a public place, they have a right to exercise their religion.

Let's apply this test to a nativity scene on public lands. Is the government establishing a state religion if I put the scene up? No. Am I freely exercising my religion if I put it up? Yes. So your rights are protected (You don't have to join a state religion) and my rights are protected (the right to exercise my religion by putting up a nativity). In a public place, a person has the right to exercise their religion.