Can a bmx hub support a 7 speed mountain bike freewheel?
You could do this by respacing a standard axle (as opposed to proprietary) 3/8" BMX hub. The freewheel thread is the same as long as the BMX hub doesn't take only metric or LHD freewheels. It's something a tinkerer might do for fun to make use of some rims. There are some issues that may hold it back from practicality:


Current standard 3/8" axle 48h BMX hubs are more or less garbage
parts. Almost by definition they only have 48h for looks at that
point, since real freestyle bikes use 14mm rear and race bikes never use
48h. There are probably pre-14mm hubs that are counterexamples, but I can't think of any that use standard axles.
The extra strength and durability of it being a 48h wheel would
be somewhat wasted given its vulnerability to bent axles, being a
freewheel hub.


Some BMX rear hubs have flange to flange distances that are significantly greater than the 57-58mm numbers usually found on 135mm MTB hubs. You'd want to avoid that, because making a derailer wheel out of one would give less lateral strength.