A couple things at play here.
First - the fork is made of metal. That is a source of noise from incidental contact, not from use. If you want to tape it up it is not a bad idea. I would leave the sharp points though, because they do serve a purpose. It also might prevent you from adjusting it.
The two points of the fork allow you to "set" the seat into the tree. The noise you'll get is if you try to change the angle of the seat or move the position of the fork left or right without loading your feet and "unsetting" the fork from the tree. If used properly, you can pivot on either point of the fork extremely quietly, smoothly, and without drawing attention. This is a huge selling point of the web or hybrid. But you need to do it right to reduce noise...
The fork needs to have the force transferring perpendicular to the tree - in other words, you can't have the fork angled up or down, and load it. It will want to slip the opposite direction with any movement from you. And it will create a really loud scraping noise - metal with your body weight behind it. There are two ways to do this - adjust tether height/position of connection to tether up or down, or if you've got an adjustable fork(not stock on the web, stock on the hybrid) - you set your tether, then slide fork in or out to create 90* angle between fork and tree. Sound complicated? It's not. Takes ten seconds. Think about it like shifting your feet on steps or your platform. If you just willy nilly slide or move them they create noise. But if you take your time and are careful, you can move, rotate, or pick up your feet without making noise. Same thing with fork.
The fork resting against the tree allows you smooth, quiet movement pivoting on either point. when you reach the end of rotation on that point, you'll need to slowly push back from the tree, reposition fork, set back into tree, and continue rotation if needed. I typically relocate fork to face an incoming deer - this allows me rotation in either direction to stay behind tree or take a shot. The fork resting against the tree is also why it's so comfortable - you can unload your legs completely.
Hope this helps.