Tiles that are produced from any one batch will always be of uniform thickness.
Marble and granite will be machined and rectified into tile size pieces and can be expected to be consistent in thickness.
With some quarried product like slate, however, there will be a variation in thickness between each tile. That is because slate and natural stone tiles is split from larger slabs. Your tiler will sort the slate by thickness before he lays it.
There is nothing wrong with mixing tiles of varying colours, textures, sizes, or thickness on a project.
As long as each tile is suited for the purpose used, thickness is just another variation. Make sure that your tiler is aware that he will have to allow for the difference in the process of tiling.
The tiler may need to change adhesives on your project to one that is suitable to be built up thicker than standard. Your local Beaumont Tiles store can help with advice on that.
If the tiler has laid the tiles without allowing for the variation in tile thickness, there will be definite steps in the floor or wall. This is not really acceptable and the tiling will need to be repaired or replaced.