I believe there is a connection, but I’m not sure it has anything to do with the “bacteria in the gut” theory. Both are auto-immune conditions, and may share certain common characteristics, which are not yet fully understood. I think I’m right in saying that MS and Crohn’s cluster in families more commonly than would be expected by chance alone, which is suggestive of a common genetic basis. This is true of some other auto-immune diseases too.
I think some treatments used for Crohn’s have also shown some promise as treatments for MS - again suggesting there’s some common mechanism.
I have both MS and Crohn’s in the family, but on opposite sides. Tragically, and very unusually, the person with Crohn’s died of it, at a relatively young age. The person with MS lived to be 87.
If you had to pick which one you were going to get, you’d assume MS was the more dangerous, wouldn’t you? But it just goes to show you can’t always tell.