I would be concerned too OP, and would, and have, struggled to maintain a friendship in those circumstances.
I know lots of people that are Christians l, but not evangelists, and although I am not religious we respect one another's thoughts and beliefs and it doesn't impact on our relationship.
I have known a few evangelical Christians though who, like the examples you state, are not able to do that, and take it to the extreme, ultimately believing that God is telling them to convert people and controlling every aspect of their lives. Each of these people has been vulnerable and in a difficult place in their lives before being 'rescued' by their church. I can understand that for them, they want to belong and feel it gives them validation but I also feel uncomfortable with the idea of them being preyed upon at a vulnerable time and 'converted' by other evangelists when they were perhaps not in the state of mind to make an informed decision for themselves. Two of the people I knew then went on to do the same - one of them, for example, taking on a voluntary position at a drop in for homeless people with the sole purpose of converting people (by telling them God was testing them and she could help them pass the test if they came to church and followed her advice etc and then things would get better for them.) It was quite disturbing to see the change in her, having previously been open minded she became someone with very bigoted views on things like sexuality. She was not allowed to carry on volunteering at the drop in but continues still to pursue similar opportunities to 'lead people to the correct path.' It's a difficult position - I feel for her as I know she is vulnerable and to some extent has been taken advantage of but I don't and won't condone her treatment of others, and whilst I respect that she has a choice of what to believe she doesn't afford that same respect to me or anyone else. It's a really difficult one. I used to work on a very deprived estate where an evangelist from the same church my friend had got involved with used to door knock on all the tower blocks and go along to groups for single parents etc to tell them to follow her path and that things would get better. What really struck me was that it was in plain sight of local agencies but nothing was done, seemingly because it was a 'Christian' organisation - if it had been a Muslim or other minority group I am quite sure it would be have stopped very quickly. I actually reported the second example under Prevent but to my knowledge the group is still present and active in that area a year later.