I'd say the worst thing the survivors do is continually subject the zombies to microaggressions and sometimes even outright anti-zombie policies that make it impossible for zombies to get ahead. I think the first thing the survivors should do in a zombie apocalypse is stop oppressing the zombies and put together a committee to view society through a "zombie lens." They should also make an effort to include zombies in their exclusionary "survivor groups."
It also wouldn't be a bad idea to evolve the definitions of words like "alive" and "undead." "Undead" and "zombie" have a long, hateful, prejudiced history as labels, and both automatically conjure up images of a person you wouldn't want to be around. Words have meanings and those meanings can be hurtful. So survivors (whatever that even means) should also set up a committee for language reform in a way that makes EVERYONE feel included. And ideally, zombies should be on the committee too. People can be healthy at any stage of death or decay. We shouldn't be telling dead people that they're unhealthy.