The thing is, each of us have lines. At least, I think we do.

There are some things that are okay, and some that aren't. Doctrinal issues are those lines for me. There are certain black and white issues that I don't want to dilute, and I don't want someone else diluting them for my children.
The fact that they aren't black or white to other people on this forum, or that other people see a different black and white is completely irrelevant.
I have to stand firm on
my beliefs, and some things aren't compromisable for me.
It horrifies me to think that my children might someday stumble back into the doctrinal darkness that has shrouded much of the church for the last few hundred years. I will do everything in my power to make sure they stay walking in the light of truth and clarity. (On many issues--and this is one of them!)
My husband was saved FROM trinitarian beliefs. He's more dogmatic than I am, believing that trinitarian doctrine is idolatry. He doesn't like to go to trinitarian churches even for special occasions.
He wrote a song shortly after being converted about coming out of darkness, realizing that the "Fullness of the Godhead was...complete in the One Who died for me." It meant a lot to him to finally understand scriptures he had found contradictory for years. My mother was converted from being a "hardshell" Baptist. The scripture that clicked for her was
I Timothy 3:16. My Grandfather was an altar boy in the Catholic church. He later became an Apostolic preacher.
All other matters aside, I wouldn't attend a trinitarian church simply because it would be a huge stumbling block for my husband.
So for the sake of our family, our collective integrity, and the spiritual futures of our children, we won't attend a trinity church. We would have church in our home (and invite all the neighbors) before we would go to an assembly that taught false doctrine, or even one that refused to acknowledge truth.
On another note, I don't appreciate churches that ride fences. There are absolutes in scripture. I think it's lame when people refuse to stand for anything at all. I'm not accusing anyone on THIS thread of doing that, but that's kind of how I see "non-denominational" churches. They're trying so hard to be inclusive of people, that they forget to include God's Word in every matter. I'm of the opinion that nearly every problem can be answered with scripture and that the Word should be consulted on a regular basis.
I'm all for finding the "purpose" of the church, for preaching the cross, and keeping the main thing the main thing. On the other hand, it can get so diluted that people aren't actually being saved--they're just experiencing a church service. JMO (and just my ramblings) Salvation still requires faith and obedience. It's not enough to be a hearer of the Word, and even a believer of the Word. You must also be a DOER.
When we hear the Word, it shows us who we are, and who we need to be in Christ, but if we don't obey what we hear, we walk away unchanged. (
James 1:21-25)