Because imposing Draconian border regimes and terrorising violence on those deemed inferior is exactly what they themselves would do.

Honestly, for a lot of rural dwellers and exurbanites, "city" is a scare word all on its own.

They're not who need to be convinced, though, it's the urbanites and suburbanites. There are more conservatives in cities than our in the country, it's just that in the country we're in the majority and in the city we're not. The urban conservatives are the target audience for this message.

It's great messaging that has no real reason against it. This is a problem for people who have power and money based on urban sprawl, and so they need some kind of argument. If they can't find one even halfway reasonable, then they must create a strawman version of the original idea. Conservatives are already primed to believe that leftists want to control every aspect of your life, and so it's a simple leap to believe this is yet another attempt at control. In turn, this reinforces that same belief for next time. It's the cycle of bullshit.

Maybe they've distorted it in the same way the BLM slogan was distorted? Like, when conservatives heard "black lives matter", it got translated to "only black lives matter" in their weird little absolutist brains. Maybe "15 minute city" translates into "you can only go 15 minutes from the bus stop or train station" for them.