I like your idea!
Unfortunately, many Christians say they are angry about LGBTQ groups supposedly co-opting the rainbow. They believe they should have exclusive use of the symbol, because the sadistic god they worship used it to promise never again to kill almost all human beings with a global flood.
Of course, progressive or more liberal Christians don't believe the Noah flood story is literal. But they're not the ones hating on Pride month.
The Christians hating on Pride month are quite proud to tell stories about the monster they worship. Their core beliefs instill a certain cruelty in them. A worshiping of cruelty. After all, they're the same ones who believe sacrificial death is necessary for their god forgive human beings of their "sins."
With a cruel set of core beliefs like that, it's hard to imagine any positive message getting across to them, especially when they already think we're stealing "their" rainbow.
But I guess the best thing to do is carry on while ignoring them the best we can, other than, of course, to watch our backs and understand they're gunning for us.