When I use, e.g. refactoring or Ctrl+Shift+arrow shortcut to select a text, I can't delete it with d as if I did it via select mode. It gets especially annoying when the plugin doesn't recognize automatic selection on refactoring. How do I fix or work around it?
I think this is depended on the ideavim impl. I am using ideavim as well, however, I don't use those arrow keys. I tested what you said, it can be reproduced here.
It seems that the c-s-arrows selection won't let ideavim switch to VISUAL mode, thus, the later actions are just executed from your cursor position, and ignore the selections. However, if you select some text with the mouse, ideavim recognizes it as visual selection.
I would suggest not using the arrows for selection any longer if you have already decided to use vim (ideavim). If this function is very important to you, you could consider reporting an issue/bug to ideavim team.