Some tabs are taller than others. It would be cool if their sizes could be unified.

Images:
image 1
image 2

The rest of the inventory is also moving down.

Ooh! Yeah the tabs move according to the inventory's GUI size, so things like double chests will move the tabs up more than single chests.

If I kept the top tabs static, then the bottom ones would be the ones moving. This isn't something I can really fix without making the tabs float above and below the GUI (instead of being connected to it).

You can use the tab and shift-tab keybinds (these are configurable) to switch tabs without having to click on the moving tab locations.

I'll look into seeing if I can find a way for them to be static

I'm sorry, I'm not exactly sure what you are asking.

Inventory Tabs are styled like the creative inventory tabs, they get taller when selected. You can use a resource pack to change this