As long as there is not a "Energy Conserving" in the API label on the back of the container. Synthetic is safe to use with wet clutches. I have used Castrol Syntec 20-50W in my 2004 Road Star and Castrol Syntec 0-20W in my 1985 400WRX Both work as they have no friction modifiers. Synthetic is best when storing for a time as conventional oil breaks down and becomes acidic. I experienced that on a project GS850G when it sat for seven years before I replaced the head gasket. I pulled the cylinders off and found the rings in #2 cylinder etched themselves into the cylinder wall deep enough to require 2 oversizes to clean up. Conventional oil breaks down after 3 months.
You can also use ATF but that is a whole other topic
You can also use ATF but that is a whole other topic