On what grounds should one uphold/deny fellowship? Is it biblical to uphold fellowship with one who is very liberal with regard to fundamentals such as soteriology and regeneration?
Well that depends first on what you mean by "fellowship." Does that mean you don;t speak to them or relate to them in any way? Or are you referring to working closely with them or letting them teach in your church? If someone holds inbiblical views, I would certainly not want them teaching a Bible class in my church or guiding the young people, for instance. But I think many of today's Christians are too quick to shun people who they disagree with. We are called to be salt and light. That means we need to relate to the darkness in some manner. That never means we compromise our beliefs. But I am quite confident in my own walk with God so I am never intimidated to sit down and talk with someone whom I believe is walking in error. How else do you help them find the truth?
I agree. When your core Biblical beliefs are shared you have grounds for Christian fellowship. There are some people I have coffee with in my home, and there are some people I meet at the coffee shop because I don’t want their influence in my home. When there is little common ground theologically you should not welcome them into your “home” as it is dangerous to the young in the faith. Where there are only differences on peripheral areas and not core beliefs, there is plenty of room to work together in the Kingdom.