When installing MDF beadboard onto a wall that is presently tiled, do the tiles have to be removed first, or can the beadboard go on top of the tiles?

I am not a carpenter, BUT:
MDF should be nailed to the studs not glued ( ? ) to tile and . .

MDF SHOULD NOT be put in in a high moisture area like the bath room. It acts like a sponge and may promote mold and mildew.

There are other wall materials intended for a bathroom.

You don’t have to but it isn’t recommended.

Read more here:

http://homeimprovement.lovetoknow.com/Beadboard_Over_Ceramic_Tile

The beadboard will not be supporting much weight, so I suspect you could get away with attaching it to the tile. But it seems a shoddy approach to me (note, I have no particular expertise except as someone who does home improvement projects on my own house). Personally, I’d pull the tile down.

You always notice MDF in a bathroom, cabinets and walls alike. That’s the part that is swollen, buckled, peeling and generally disintegrating.
If you like the beadboard look how about something more waterproof and go at it with a router?