I suppose each of us has that thing that becomes a "stopper" as we consider church affiliation. Truth be told, I am somewhat conflicted about TEC's stance on LGBT issues. On one hand the Bible says what it says. On the other hand there are LGBT people in my parish who I like and who most would agree are devout and sincere Christians if it was not for that one thing in their life. I was preacher's kid long enough to know we already have other sinners in the pulpit, including the unrepentant.
The bottom line, I suppose, is that there are other issues that were more important "stoppers" for me than this. For example, I am strongly against closed communion. I disagree with re-baptism. I don't believe in the immaculate conception, the assumption of Mary, purgatory, or church hierarchy sweeping clergy's child sexual abuse under the rug. Therefore my list narrowed greatly. Gone from it were RC, EO, & LCMS. And there were things that attracted me, most notably the beautiful liturgy and worship opportinity TEC provides.
I think I am not going to be judged by what my church believes, but for how I live and act. I encourage OP to carefully consider her "stoppers." Is this her most important one?