There's been lots of recent stories of teachers refusing the call kids by their preferred pronouns, for one. But also, I think you're trying to be more rational than these conservatives are. They don't need there to be a difference in how they work with someone to refuse to do it. Some will literally claim it's against their religion to be involved with an LGBT person at all.
Stuff like education is an obvious basic right, yeah, but there's so much fuzziness. Should the only store in walking distance be able to refuse to serve you? Especially in small towns where there might only be a single business providing a service, they can easily make the area effectively an unlivable area for whichever group is the current focus of conservatives.
Plus there's the good ol' paradox of intolerance. By just allowing people to discriminate, it spreads. When it's acceptable for one business to discriminate, it's more likely others are going to adopt the same stance. More people will be taught their intolerance. It's basically a social illness. Much like a real illness, that needs to be isolated and prevented from spreading.
Do you think it's a good world if someone, say, can't use the nearest small grocery store or has a 50/50 chance that any given taxi will refuse to serve them, leaving them stranded for longer and regularly late as a result? All because maybe they look gay or trans or Muslim or whatever the right wing media is currently drumming up fear towards?
Your comment is about the perspective of the person providing the service, but what about the people being affected by the discrimination (who are often more vulnerable in the first place)? Do you not care about their experience? Their ability to experience the same quality of life as everyone else?
And sure, the world is a mean place, but why defend that? Why not try to make it at least a little bit better?