Should I avoid hard-packed crusher dust trails with my hybrid?
You are absolutely fine riding the Trek FX 7.2 with the Bontrager tires on that trail. That gravel surface is not any worse than rough, worn tarmac so go ahead and enjoy those trails.

You don't really need much tire tread (or any) on flat crushed gravel trails, 35mm wide tires have plenty of volume. 

Be aware that you will have less grip, both in cornering and braking. Try running slightly lower pressure than you would on the road. Avoid big bumps and potholes. Carry a spare tube, tire levers and CO2 inflator or mini pump in case you get a flat.