No. Having a Constitutional right to free speech means you can't be arrested for speaking, but that doesn't apply in private organizations. You, for example, have no Constitutional right to come into my house and protest something. I can throw you out without facing any penalties and if you refuse to stop, I can have you arrested. Now, if you stand on the public road near my house with a sign and shout that Joe Biden is a poopy-head, you won't be arrested and I can't legally stop you. Hasn't anyone explained to you what free speech actually means?
There are many intrusions on the First Amendment and on one says it's absolute. What you are doing is taking it to an absurd extreme to claim basically that anyone can say anything at any time with no legal repercussions. You have, for example, no Constitutional right to go into the Senate and yell that your dogcatcher votes Republican so you hate him. You would be ejected rapidly and forcefully. You can't make public threats on a politician's life without legal consequences.
The bottom line is, you have no Constitutional right to invade a church and protest. They have the right to control what speech happens in their building. Have you tried doing that in a mosque?
1. Show us the written documentation. If it's a formal policy, it should be written somewhere so we can see it.
2. Administrations routinely decide what they are going to prosecute and what they will not. Case in point, cities and states that announce they are going to ignore and violate federal law should land mayors and governors in hot water but usually do not.