Local and federal authorities are investigating after a group of anti-ICE protesters crashed a Minnesota church service ... and one of the demonstrators tells TMZ she'd still do it all over again.

Here's the deal ... the DOJ and local police are investigating after protesters interrupted a service at the Cities Church in St. Paul ... which is getting major headlines because Don Lemon was in the mix live-streaming the incident.

Chauntyll Allen, leader of Black Lives Matter Twin Cities, who was among the group, tells TMZ … the jarring protest inside the church was necessary to make clear to the parishioners that having a pastor who is also an ICE official is unacceptable.

Chauntyll, who's also a St. Paul School Board member, argues the community is being ripped apart by ICE … so the group disrupting a church service -- and upsetting some parishioners -- in comparison is pretty small potatoes.

The protesters have been dragged by people on the Right for going inside the church ... but Chauntyll tells us she doesn’t think a line was crossed … and she would do it again if given the opportunity.

As for the threats of possible criminal charges ... as you can see in the video, Chauntyll couldn't care less, and argues the feds have vastly bigger fish to fry.

We spoke to a Cities Church member who feels the complete opposite ... and who welcomes authorities sending a message that this type of behavior is unacceptable. And it seems President Trump agrees ... sharing a social media post that Lemon specifically should be locked away.