As the title- which glue will stick polystyrene to mdf without melting the polystyrene?

Cheaper the better!

Pretty sure you need to use dilute PVA glue on MDF first to make anythign stick as it will just absorb the glue into it- been a while not certain
I am also pretty sure PVA glue will stick to polystyrene without reaction
its also cheap

Sealant will also work but you will either need to use the blob technique or loads of it and not going to end up cheap depending on size of sheet/mdf

no need to dilute PVA, imo.

look at contact adhesive. had to do something similar for a display last week. sheets of cork onto board for a pin wall.

PVA will work just fine. Silly cheap so can use loads

Copydex used as a contact adhesive.

I usually use polyurethane wood glue but you need to have plenty of weight on the polystyrene as the glue expands otherwise. The poly will be well an truly stuck on there though as the glue really gets into the nooks and crannies.

You’ll end up redoing the PVA in about 10 years if my loft hatch is a good example. Hardly onerous though.

Spray glue, the stuff you use to stick carpet to metal van walls. Cheap as chipps.