When creating websites with Joomla, I use underscore _ to module class suffix thus seperating names from moduletable so to make it obvious like moduletable_sidebar.

However, I just realized that K2 makes the same input as single classes like _sidebar which makes them invalid I guess as it is not allowed.
So, is my option to change that underscore to simple dash or is there another way to prevent it?

You can change that in your template overrides either for the component or the modules.

K2 uses the classes separately because nowadays there is more need to use multiple classes than just one.

Ok, that's fine, but will do any harm to my code if I leave them as it is? I don't need these classes at all.

I don't see how you will be having issues. The only thing it will be affected is your css maybe.