Proper HDTV settings for Xbox360 on 32 inch screen?

Ok, so I've got a 32" Emerson LED TV that has HD capabilities, however, when I set my Xbox360 from 480p to 1080p, it automatically goes into widescreen mode. This is slightly problematic because it causes the HUD on one of my games (GTA V) to noticeably shrink to half in size, and also slightly deformes the graphics (makes everything slightly taller in height/shorter lengthwise).

Is this normal? Or does the screen need adjusting?

I want to keep it on 1080p to be able to play local multiplayer on Minecraft without the hassle of redoing the graphics again afterwards.

This may not just be the tv. Try adjusting settings on your Xbox.