Minecraft 1.9, Forge 12.16.0.1867, moreoverlays-1.2-mc1.9
This happens even with JEI closed so it's probably not another mod's OpenGL issue.

I know, but I don't think that there is a render event after the gui is rendered and before rendering the tooltip.

Rendering the tooltip again is how I got around a similar issue in JEI too, before I added a new Forge event at the spot I wanted to render. I think this fix will work fine.

You should use the new GuiUtils.drawHoveringText method in Forge instead of your GuiUtil class though.

Thanks for the quick fixes!