Looks like you have a nice collection. I strongly recommend using 2x2 cardboard flips with mylar windows. It is the next best thing to being able to touch the coins directly. Moreover, it also slows down environmental damage, especially for silver and copper, and protects against scratches and damage if you accidentally drop a coin.
As Peter pointed out, some materials in your cabinet may be harmful for your coins. Maybe a little research into the back-material of your cabinet is warranted. Valuable coins need to be taken care of!