How MUPs work. Cyclists need to accept that a MUP is, by definition(name), not a bike path.

Cyclists yield to all.
Roller bladers yield to the below.
Runners yield to the below.
Walkers yiled to the below.
Families with small children yield to the below.
Equestrian trail riders.

See how that goes? Cyclists yield to all as they are the fastest and can cause the most harm.