Commando gear cannot be worn by Engineers, Engineer gear cannot be worn by Operators, etc. There are universal gear that can be worn by everyone, though, such as the following weapons:

Silenced A-OK
Xtended A-OK
Scoped A-OK
PlasmA-OK
Silenced Repeater
Velocity Repeater
Xtended Repeater
Scoped Repeater
Reaper Pistol
AMP-X Pistol
Scoped AMP Pistol
Plas-AMP Pistol

You can still have a hybrid-type of character by having any combination of STR, DEX, or INT though.