That depends on the non-denominational church in questions. There are some that are very orthodox and bible believing and there are some very heterodox. With regard to the SBC, it's interesting. A year ago our Baptist church made a proposal to the congregation to affiliate with the SBC and scheduled it for a vote. I started researching them. Their statement of faith and theology is rock solid. But I stumbled onto the writings of its influential officer Russel Moore. The more I read from him the more disenchanted I got. I came out against the proposal and communicated to fellow parishioners the reasons why. I also urged them to investigate themselves. The proposal was defeated by a wide margin.
So, what was it about Russel Moore that disappointed you?
Russell Moore is a big reason I left. SBC has an identity crisis as conservatives are disillusioned with the leadership, yet the public (and MSM) view the SBC as conservative.