Open wraps are better for younger locks. Once they mature, you can do closed wraps.
While the thread tends to stay wet longer than your hair does, open wraps allow for enough ventilation that you won't run the risk of mold. Closed wraps, if left on too long, can cause mold.
Most people try not to leave wraps on for months on end. They tend to get tangled in with the lock and are a pain to get out. I learned the hard way. If you only leave them on for a few weeks, they are easy to remove.
If you find that gunk is getting stuck in your hair, it's probably not from the wrap, unless it's lint, which can get snagged in. Most of the time, just removing the wrap will pull out most of the lint, anyway. If not, you can gently pluck it out with your fingers, or gently with tweezers. if it's stuck in your lock nice and tight, it's just something you may have to deal with. I have blue fuzzies all over my locks from my favorite hoody. They aren't as noticeable to others as they are to you