I don't think you could solve gluten intolerance but just improving your gut microbiome, so they're probably not related.
Other gluten intolerance is probably not gluten, gluten is just a close enough proxy. Could be FODMAP + IBS or maybe some other sensitivity.
We also don't really understand why things like a FODMAP diet work. It's not that feeding your gut bacteria is bad, it's actually pretty good. But for some people it's bad, and they get symptoms they attribute to gluten intolerance.
Legumes, onions, whole grain etc that are high FODMAP are good for you. Fiber is good for you, it lowers your risk of metabolic diseases and helps your digestion. But, for some people, it's bad for their digestion. That's weird.
So all that is to say that, while gut bacteria matters, it varies person to person and we can't definitely say what food is good for the microbiome and what isn't.
Seems extremely unlikely. Of someone is eliminating gluten they from their diet they usually aren't also eliminating dairy, legumes, and other high-fodmap foods; gluten-free is restrictive enough already.
The only other sensitivity I could think of in which this makes sense is wheat sensitivity (but not other gluten containing grains which are less common).