Is it okay to glue mirror cabinet to tiles ? (IKEA LILLÅNGEN)

Your problem is probably due to impurities/dirt on the tiles - you really need to get them clean.

I used isopropyl alcohol on mine, and scrubbed them hard. As soon as they dried I applied an epoxy and the hooks are probably now attached to the tiles more strongly than the tiles are attached to the wall :-)

In most cases, a silicone based glue would adhere fairly well to most tiles. On smooth tiles it can be removed with a razor blade. On rougher tiles, a blade and a wire brush can get it off. The tiles need to be thoroughly cleaned before using (as with any glue).

This is not as strong a bond as epoxy or construction adhesive, as suggested by Chris Cudmore, but is more easily reversed if necessary.

Because it is not as strong, I would limit it to lighter items, like the soap holder you describe. It is definitely not suitable for a grab bar or other attachment that needs certain hold. Safety items need to be attached to structure, not glued on.