I'm not sure what rights Don Lemon has as a journalist, but according to the definition of the FACE Act I read below, the protesters are in violation of the FACE Act. I would also question what access "rights" a journalist has when the access was created by an illegal act. As you stated, trespassing at a minimum. Either way, they have zero right to interfere with a worship service on private property.
Edit: There are two very incriminating videos (made by Don Lemon) making their rounds on X that show him present in the planning of the protest and advocating for the church protest once inside. His intent was not to be there as a journalist reporting. He did more than just trespass...
www.law.cornell.edu
There are relevant legal minds who don't agree:
NYT Gift Article
...
After considering the complaint, Judge Micko found there was probable cause to issue warrants for three of the suspects — Nekima Levy Armstrong, Chauntyll Louisa Allen and William Kelly — all of whom were ultimately taken into custody on Thursday. But he refused to approve warrants for the other five people, including Mr. Lemon, who had been working as an independent reporter, and his producer, the unsealed court papers said.
Almost immediately, the U.S. attorney in Minnesota, Daniel N. Rosen, who was appointed by President Trump last year, notified the district’s chief judge, Patrick J. Schiltz, that he wanted another judge to review Judge Micko’s decision — a highly unusual move.
Typically, Judge Schiltz wrote in a letter to the appeals court, if the government is unsatisfied with a magistrate’s refusal to sign warrants, it can either “improve” its affidavit making the request and present it again, or it can set aside its criminal complaint and try a different way to charge the suspects: by seeking a grand jury indictment.
“It is important to emphasize that what the U.S. attorney requested is unheard-of in our district or, as best as I can tell, any other district in the Eighth Circuit,” wrote Judge Schiltz, a staunch Republican appointed by President George W. Bush. “I have surveyed all of our judges — some of whom have been judges in our district for over 40 years — and no one can remember the government asking a district judge to review a magistrate judge’s denial of an arrest warrant.”
Moreover, Judge Schiltz wrote, three of the people whose warrants were denied had not been charged with committing any violence, but at worst had been accused of “yelling horrible things at the members of the church.” He added there was no evidence that Mr. Lemon or his producer had engaged “in any criminal behavior or conspired to do so.”
At first, Judge Schiltz sought to take a measured path in response to the request by Mr. Rosen, a longtime commercial litigator who had little experience in prosecuting criminal cases when he took over as U.S. attorney in October.
Noting that the request was “unprecedented” and had prompted “strong and differing views” from his fellow judges, Judge Schiltz told Mr. Rosen that he would not decide what to do about the warrants until he had discussed the issue at a meeting with his colleagues scheduled for this past Wednesday.