Does “Logan” count as an X-Men story where there’s been progress on mutant rights? No-one except the villain has any prejudice against mutants.

Logan is an X-Men story where the X-gene has been bred out of the population through tailored genetic diseases distributed through the food chain so that the military-industrial complex can monopolize and patent the X-gene to breed slave-soldiers. I wouldn’t call that progress. 

In that scenario, there’s not much prejudice against mutants, because the popular perception is that there are no more mutants – as is stated by the radio host that Logan is listening to early on in the film when he’s driving his limo.