They won’t let us ignore them. We are being made to care, to accept, to endorse.
There was a time, not so long ago, when I personally took a "live and let live" policy towards activists, gay activists in particular. They called for "tolerance" and I was tolerant. Mostly because I didn't care about their causes.
Now, as you point out, they're calling for forced acceptance, even forced celebration of their causes. "Do this, or I will ruin you. Because I can." is approximately their position. So, now I'm being forced to pay attention, to care.
I may be wrong, but I think that activists - gay activists, specifically - won't like it when conservatives start to pay attention, to care about their causes. I suspect that they'll want to dial the clock back 20 years to the laissez-faire attitude that I, and many others, held.
Because it won't end well, for anyone.