As an autistic person with a severe gut disorder (ulcerative colitis - one of the risk factors is a diet high in processed foods) I think it's very likely that autism causes gut issues, including microbiome issues. If you eat mostly the same foods, the bacteria that don't feed off them will die off, and you get a less diverse, weaker microbiome. I'm not a microbiologist but I have personal experience here because my UC forces me to restrict my diet in strange ways when I have active inflammation (like for months or years), but I can later reintroduce foods, but then they're harder to digest for a while because my microbiome has changed. So it makes sense that since most autistic people have more limited diets due to routine, obsession, or sensory issues, we would tend to have worse gut microbiomes.
People who view autism as a disease that might be curable will see any connection as a potential cause, even though in most cases the causal relationship is more likely to be in the other direction. It's so frustrating.