I know what you write is true because I grew up in that world too. But the dissonance and internal inconsistency are so stark. Evangelical Christians, among the Christians most powerfully opposed to respect and acceptance of LGBTQ people, believe in salvation by faith, through grace alone. Works can't save you. Nobody can live without sin, which can even be unconscious.
Hence, the sinner's prayer and acceptance of unearned salvation.
That's one thing, one dissonant thing. The other big one is the constant fluidity in the Evangelical world of the definition of sinful acts. When I was a kid, to name a trivial example, dancing to Elvis Presley music was shockingly sinful to most Evangelicals. Today, it's a quaint and nostalgic practice. So, here's the thing: Evangelicals can agree to disagree about what equals sin. Most sin, (like lack of charity) they ignore as a personal issue that's none of their business, because ... the whole "salvation by faith through grace" thing.
With other "sins" like homosexuality, however, they act suddenly as if disagreement is not allowed and that salvation must in some sense be earned. Naturally, they choose sins that are traditionally despised in conservative religious circles and so not apt to be controversial in their congregations.
None of it makes coherent sense, but here we are.