Well, in our church, they would have to shake at least 20+ hands before they could even sit down in service....so they might get tired of that pretty quick

They couldn't just "sneak in"...so they would have lot's of attention and I'm sure everyone in church would figure out what they were up to pretty quick,

since they would definitely "stand out in our crowd".
So, if they still decided to go through with their protest....so what? It's just a bunch of noise...nothing of any consequence in the end. We would invite them stay for service. Ha!!! Our shoulders are big enough to handle a little noise during church for goodness sakes.
Like in the story, the protestors would probably scream out their viewpoint and leave.....to which we would just shrug and go on with service...with a special prayer for them of course.
If they decided to stay for service (highly unlikely), I'm sure the Pastor would preach something like "Salvation from denomic influences"; coupled with prayer. We would even ask if we could pray with them. But that's all imaginary, because the protestors would never stay anyway.
If the protest was in the parking lot. Then we would go outside and welcome them to service...if they didn't want to come in, then we would go back inside and start praying down conviction on them. I'm sure they would quickly get bored if we weren't confrontational and go away. Our weapons of prayer are greater than words anyway. We might even look upon the situation with joy...
The police only need to become involved when there are weapons or violence (including defacing property) involved. That is a civil matter.
Not the same situation, but one time, the old church we used to worship in backed up to an alley in an older part of town. It seemed that during service, someone would throw small parking lot pebbles at our back door (which opened into the sanctuary) during service and run away. We didn't know who did this for a while, until one time, it happened during daylight right before service and I was standing at the door.
I quickly flung the door open and saw they were children (which we suspected anyway) and stepped out and happily and in a very friendly manner invited them to church. They didn't come...but they did quit throwing rocks at our door. Ha!
