Most FWD stick shift cars use a cable shifter similar to the mechanism that moves outside rear-view mirrors…When they wear or are incorrectly adjusted, shifting can become vague and difficult. You can test the clutch for “dragging” by shifting into reverse…It should slip in with no gear grinding. If it “fights you” going into reverse, then the clutch or its linkage has a problem…
There is a set procedure for troubleshooting, testing and adjusting these shift mechanisms…And yes, loose or broken motor mounts can play a role here…