Sorry if it isn't the best place to ask about draw.io, but I'm really stuck here.
It seems to be new addition, because it was working just fine a few months ago. When I try to connect two objects, it changes node on its own to make connection shorter, even if it clips with other objects. Here is what I'm trying to do (it won't let me though):
Here is what diagrams.net does instead:
It's one of these moments where software tries to be smarter than the user and fails miserably.
Is there a way to bypass it, or I just should find alternative website?
Well, not sure where you have the problem. I get the same behaviour as in your second screenshot but by moving the anchor of the line, I get what you have in the first screenshot.
See animated GIF: