You're ascribing far too much logical thought to it. I've argued with her about editions and translations of the Bible. It's purely irrational attachment to the idea of the Bible that her church uses as the indisputable and unchanging word of God. Which is a shame, because she's an otherwise genuinely intelligent woman.

At least it stops at "I don't believe in or support gay marriage, but gay people are people and should not be mocked, harassed, or excluded, as we are all sinners and should not judge one another."

Which is more I can say for most fundies.

This often gets said but despite wanting it be true it doesn't really bear out. There are ways of deconstructing "man shall not lie with man" to the point of being unsure if it's prohibiting male male sex in general or homosexual temple pederasty specifically. But it's a little beside the point because the Torah also tells the Jews that the meaning of Torah would be plain to them, and general homosexual prohibition is what they always understood by it. Hopping to the new testament people often say Jesus didn't address homosexuality, but he frequently condemned "debauchery" which is not how we'd refer to homosexual acts today, but debauchery is just a translation of the Greek "porneia" which meant unlawful sex as other ancient sources show and did include homosexuality as far as the Jews would have understood it (edit: clarified wording here). There are other oblique arguments, like Jesus saying marriage wouldn't happen in heaven because everyone would be like the angels (who are all male), which implies a line of thinking where male male marriage is "obviously" not possible. And then you have a similar argument to the one employed by the Jews, that the new testament states the holy spirit would lead the apostles in "all truth" and the early church was unambiguously against homosexual relations.

I think the modern church should be accepting of all sexualities. But that's more because I think the modern church should not be so wed to the Bible..