I'm trying to align items with a diagonal wall but they will not sit next to it, standing far enough way to prevent doors next to them from working. Moveobjects doesn't seem to be working here, I can move the objects in steps of about half a tile but that doesn't help. What's wrong?

Note the shower stall needs to be moved also, parts of it are visible on the other side of that wall.

This is really annoying thing when placing objects diagonally

When you hold the ALT button in the same time while moving objects, it allows to move them around, ignoring the grid - this will help you to place the cabinets on the wall instead of having this gap, while they are diagonally aligned, or even rotate them at different angle than the usual 90 and 45 degrees. Note that this method doesn't work on objects that are designed to snap on the wall, like the toilet or the sink in your case.

You could try to remove the second counter before moving the first one. They are coded to snap to each other, so it will always move in relation to that other counter.

That was a major part of the issue, two pieces near each other were interacting as I tried to position one. Thanks for the idea.