When religion is used to shield people engaged in administering harm from accountability to the broader community, perhaps we need to stop and ask if we aren't on the wrong side of things and what kind of witness that is demonstrating to the world?
You do not have the moral or legal right to trespass in my church, which is private property, or impede entry to it, because you think a member of my clergy might be an officer of a law enforcement organization conducting law enforcement operations (that were conducted, I would note, even in the Obama administration as a matter of course) you find morally objectionable.
The reverse is also true; I do not have the right to trespass in your church because your church might have a member of clergy who promotes the continued legalization of abortion and euthanasia, or who is, for example, a prosecutor who is conducting prosecutions of Christians who obstructed an abortion clinic entrance (which interestingly is forbidden by the same bipartisan law that also forbids obstructing churches, which was essentially a bit of that parliamentary jiu-jitsu that in the US we commonly refer to as “log rolling” or as “I’ll scratch your back if you scratch my back” to use a particularly colorful metaphor from the 1990s.
The absurdity of all of this is that the protestors in question would have been entirely within their constitutional rights to protest on public land across from the street in a manner that was not disorderly. But the right to freedom of speech does not extend to preventing the speech of someone else, by entering into, for example, their workplace or their place of worship, and disrupting whatever they are seeking to do, because you suspect them of being a member of a law enforcement agency you have moral qualms with.
The fact that this issue is even controversial I find appalling; as if trespass and disorderly conduct is now regarded as acceptable behavior in the consecrated precincts of a church, even one which I personally would not patronize, for said church is not Orthodox. But the principle holds.
Suppose, for example, because some churches in my denomination, the Orthodox Church in America, serve predominantly Russian communities and are called Russian Orthodox, despite the fact we were granted autocephalous status by the Moscow Patriarchate in 1970 and thus have no connection with the MP or with anyone involved in the ongoing tragic fratricide of Russians and Ukrainians, that some Ukrainians were to protest in our church under the assumption that because it says Russian Orthodox therefore that means the priest is part of the Moscow Patriarchate and therefore presumptively a supporter of controversial Russian foreign policy?
Is that to be the next dish on this buffet of bizarre and grotesquely disproportionate behavior that I am supposed to smile and quietly endorse as the apex of free speech in Western civilization?
Or for that matter, suppose feminists were to descend upon my OCA parish because it is widely said and believed by many in the liberal mainline churches that the majority of converts to the Orthodox Church are men who are misogynistic and opposed to the rights and freedoms of women? (the large number of single women converts and the importance of women in the Orthodox church notwithstanding, even, I would note, within the Old Calendarist churches which are more likely than canonical Orthodox churches to attract the vocal minority known as “Orthobros” or in the previous decade, as “Hyperdox Herman”, notwithstanding? Since it would seem according to that group that Orthodox churches are arguably harboring men engaging in harm to the wider community through various acts of callous and disagreeable behavior with respect to the fairer sex?
I should think not.
No, your first ammendment rights do not entail infringing on mine, no matter how noble or ignoble the cause, nor vice versa. Churches, synagogues and mosques and other religious buildings are sacred places, lawfully protected, but any private place can prosecute people who refuse to leave after being asked (this is called having someone trespassed and is a daily occurrence, frequently happening on airliners, for example, when flight attendants realize a passenger is intoxicated and inform the captain, who concurs with his cabin crew that the aircraft cannot safely push back with that person on-board, which requires calling the police to remove them.
The principle of unauthorized protestors in worship services at its core boils down to that basic principle combined with a bit of the Golden Rule and also the concept of respect for the rights of others. There’s also the idea of due process - accosting someone because you think they are affiliated with a law enforcement agency you have issues with is in and of itself morally dubious activity. It could very easily constitute slander, if one were mistaken about the question of identity, which we must admit is always a risk when doing that sort of thing, and which I would note was regarded by the early church fathers as being a sin akin to murder, a sin of particular heinousness. Indeed slander is one of the very few things I know of that most Orthodox clergy will penance someone for.