18mm plywood (~3/4" for those using imperial units) is plenty thick for a cabinet door, even if it's 8' tall.
Because plywood is made up of plys of wood laid down in alternating directions, it is much more stable than solid wood would be and is much less likely to warp over time than solid wood.
I would recommend that you get high quality "cabinet grade" plywood for this project. Standard building plywood in 3/4" thickness is usually made of 5 plys, while cabinet grade is usually 11-13 plys. More plys will give you more resistance to warping. Additionally cabinet grade plywood is made from higher quality wood with fewer voids (holes in the plys) and those that are there are filled with a tan colored epoxy so they don't leave holes in edges should you happen to cut into one.
Cabinet grade plywood will also come with some sort of nicer wood on the surface plys. You can get Baltic birch, Oak, mahogany, maple and other woods on the surface of the plywood, while the inner plys are made of a cheaper (but still limited voids) wood.
Note that any 2.5' by 8' door of any construction can warp over time. There are things one can do to minimize it, and using 18mm plywood is one of those that will help minimize warping. Don't hang heavy suit bags from the outer edge of the closet door while you're packing, don't let kids hang on the doors, keep a reasonably stable humidity, don't splash drinks on it, are all things within your control that will help. However, wood is a natural product and warping can happen. It's highly unlikely, IMHO, that your doors will warp significantly any time soon.