I don't know how it is in Czechia, but here in the US, we have a long and storied history of suburbanization, white flight, redlining, exclusionary covenents and discriminatory mortgaging.
The result is entire generations of people who grew up in suburban sprawl, isolated away from anyone who didn't look like them. I don't expect to be able to convince those people to suddenly turn over a new leaf - if anything, the argument was lost long before I was born.
You cannot make public transportation both useful and sufficiently sanitized to where these sorts of people won't be bothered. It's an impossible standard - at least for a country as diverse as ours.
At this point, what is there to lose by speaking the truth?