There are a few basic elements to any quality tile or natural stone installation, with the most important being the stability of the installation, so the tiles do not crack or pop up from the installation area. For this reason, there are several acceptable underlayments you can use; along with their counterparts, they provide a solid base for tile. Plastic is not one of those things, and tiling over a plastic tub surround equals disaster waiting to happen.
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A key part of the installation is the adhesion of the tile to whatever mortar or adhesive you have chosen to use for your project. Unfortunately, none of the adhesives and mortars that are manufactured for use with tile projects are meant to be used with a plastic-based surface. As a result, the normal method of applying these materials will never work because they won't stick to plastic.
The grout joints need to have a fairly stable surface to stand up to the test of time, and if too much movement is present, the grout cracks out of the joints. In addition, thinset mortar needs relative stillness for the mortar to retain its bond to the back of the tile; if too much movement is present, the bond will break and piece of the tile will come loose, falling off or popping up from its installation area.
There are a number of specialty mastics sold that can work for linoleum or laminate surfaces, and there are specialty thinsets and mastics designed to withstand extra movement, but they are still not rated for use with plastic. While you might think that regular thinset mortar or adhesive can be used, only epoxy will bond tile to plastic and metal surfaces, but, generally, a tub surround isn't an acceptable surface.
With plastic tubs there is one reality: The tub will move every time it is filled with water, and even more so when the weight of a human body is present. There is always movement in a plastic tub, which means this movement is always transferred to the tub surround. Any tile you might have installed on the surround will fall off the plastic within a matter of weeks, as the tub goes from full to empty, to full to empty, and over again.