The doors look like vinyl wrapped MDF. In which case they were almost certainly manufactured by spraying a heat activated PUR (polyurethane) adhesive onto the MDF, stretching the vinyl wrap over the top and bonding and shrinking the vinyl onto the face of the door blank in a heated vacuum press. The protective layer is often a very thin film of (I think) PVC with a light adhesive coat on one side, however, this layer is already attached to the vinyl when it goes into the press, so it has to have a higher melting point than the PUR which is used to attach the vinyl to the door blank - therefore if you can heat iut sufficiently to soften or melt it you will almost certainly delaminate the vinyl, or at least cause it to bubble. The PUR adhesive used on the vinyl can actually be reactivated by applying the right amount of heat (generally somewhere between 85° and 140° C) - which is why if you station a kettle just below the edge of a kitchen door all the time it will eventually either bubble or delaminate., It's also a very good reason why you should avoid applying too much heat to this type of kitchen door with a hair dryer.
What I've done in the past when trying to remove this sort of coating where the doors have been stored (for months rather than years) is to cover the area I need to remove with brown parcel tape (leaving a rolled over end stuck to itself forming a sort of tab at the edge), rolled on with a little wallpaper seam roller to get a good bond (the edge of an old plastic bank card may also do). I then gently pulled the lot off by rolling the protective coating back on itself (i.e. through almost 180°). This often works because parcel tape has a stronger adhesive than the protective coating, but it isn't 100% guaranteed. Qhatever you do don't stick the parcel tape down onto the door's vinyl as it can damage it
Whatever you do, if you do decide to try solvents - avoid using acetone at all costs because acetone dissolves PVC aka "vinyl". If you need to go down that track I'd consider starting with something like WD40 on an out of sight edge, but that would really be a last resort for me
