I have also found it very easy to accidentally pull the anchor lever when I meant to climb up the ladder, releasing me from the island I'm on, even if I didn't want to leave. I can see two possible solutions for this:
1. Make it that a window pops up (are you sure you want to leave this island?) and you have to click "yes" to continue. However, this would be clunky and likely annoying for people who do not have this issue.
2. Make it that if you pull the anchor lever again after you leave (probably with a time limit of like 5-10 seconds), the ship immediately anchors back down. I prefer this one because it doesn't inconvenience players who do not have this issue.