I shot a mulie/whitetail hybrid in CO (verified by a tissue sample taken by the CO DOW) about 25 years ago. So that cross breed is possible but I don't think they would cross with axis.
Taking to biologists it’s typically a whitetail buck breeding a Muley doe.
I ran across a herd of mule deer does in west Texas that had a single WT doe that hung with them. Apparently she had for years.
I was always curious if a muley buck ever bred her successfully?