Three things need to be said:

(1) There is a distinction between opposition to homosexuals and opposition to normalization of homosexual sexual activity.

Both sides conflate these two kinds of opposition, and this is a mistake. On the pro-gay side, many believe that merely to have same-sex attractions is to be pro-gay, while many on the anti-gay side believe that merely being homosexual represents an attempt to usurp moral sexual conduct.

What you describe looks just like a case of such confusion. They see someone who looks or acts homosexual, and feel like welcoming them entails welcoming something morally wrong into their lives and community, and quite understandably chafe at the prospect.

The solution is to bring the distinction to light. To say "Yes, we welcome you, even though we do not agree with some of your choices." That many Christians are doing this is a nice segue into the second point.

(2) Namely, that many Christians are, and always have been welcoming of gays while rejecting homosexual sexual activity. But they don't receive the attention they deserve. The media loves to focus on the worst of the worst, and that means Westboro Baptist get more attention than Johnson Ferry Baptist.

Here, the solution seems to be to acknowledge the bias the media and society imposes on us. To acknowledge that we're so focused on the negative that we don't look at the positive of the big picture. To acknowledge that perhaps we don't want to acknowledge the good when we gain so much political and ideological traction from focusing on the bad.

(3) Conversion therapy doesn't entail that "Christians are against homosexuals." And there's nothing necessarily wrong with conversation therapy either, if it is studied objectively, backed by the science, practised safely, and people enter into it volitionally.

I think these three points adequately cover what you have to say. I'd say (2) is probably the most important.