Works for me.
The Bible verse you quoted is in context of the church; there are those sowing false doctrine. They are to be avoided. Actually, they are to be kicked out.
I think it is an incorrect stretch to interpret it to mean that we can’t have any relationships with liberals.
I do think you are free to disassociate with liberals if you want to, of course. Sometimes that wins people over, when they see how strongly you feel.
Other times it is best to continue the dialogue. Not everyone at FR has been a conservative all their lives. Many of us were persuaded to become so in one way or another.