Not all morals or beliefs have to be unshakable or viewed as morally reprehensible for disagreement.

The tweet suggests the sample group disagrees with this statement.

I think you’re expressing the general consensus: people get a lot of their morals from their environment, but there’s some stuff that’s universal/non-negotiable; and we should be able to find common ground with that.

At least, I think that’s the general consensus. I’ve gotten into trouble with that assumption though.