Can we actually get shut down like parler? Is that possible?

As long as the Twetch interface is hosted on third party servers, sure it can be shut down just like Parler.

Thats discomforting

Well yes but the fundamental difference is that all the data/content would still be stored on a, supposedly, immutable blockchain. Twetch is just an interface that displays the data in a user friendly way.

There is talk of running your own twetch instance, eliminating 3rd party.

That seems like a sensible idea, at least to have that fallback option when for example the Twetch app would be banned from app stores or worse.