If anything, LLM's seem more resistant to propaganda than any other tool created by man so far, except maybe the encylopedia. (Though obviously this depends on training.)
The good news is that LLM's compete commercially with each other, and if any start to intentionally give an ideological or other slant to their output, this will be noticed and reported, and a lot of people may stop using that LLM.
This is why the invention of "objective" newspaper reporting -- with corroborating sources, reporting comments on different sides of an issue, etc. -- was done for commercial reasons, not civic ones. It was a way to sell more papers, as you could trust their reporting more than the reporting from partisan rags.