As Preferred Browser command I have set: palemoon -P default "%s". But that does always ignore the -P option and starts the last used profile. Doing the same palemoon -P default "%s" in a terminal works correctly and opens the default profile. There was some bug 2947 reported 10 years ago, maybe related. This is exo-0.11.2 on Gentoo.
Sound like the same problem as #9427 : exo-open doesn't pass parameters correctly *** This bug has been marked as a duplicate of bug 9427 ***