Best adhesive to bind flat acetal/perspex splashback to plaster and/or old tile adhesive?

stixall would work well. A bit more pricey than no nails,but better grab

 

Soudal crystal? https://www.soudal.co.uk/sites/default/files/soudal_api/document/F0035115_0001.pdf

 

Why don’t you just stick the Perspex panel over the tiles (after suitable pre)

You say your not keen on removing tile adhesive, plus you can never tell how cleanly the tiles come off until you start

Issue is ( as I see it) the Perspex is best going over a solid, flat surface - you may end up with a relatively flat surface if the tiles just pop off but…..

If you kinda use ‘dot and dab’ method with blobs of adhesive which allows you to level the Perspex, then you have voids behind which may allow the Perspex to flex

I would consider cleaning tiles then simply bond the Perspex to tiles using decent quality silicone

 

Whatever method you decide to go with, remove the toilet (if you can ?) to gain better access and make the job eaiser / better finish

However long it takes you to remove the toilet, will probably save youn this time plus more in prep work and fitting the perspex - (not always an easy job though I realise, depends how spigot conects to soil pipe)

As your going over the old tile adhesive, I would prime the tile adhesive with SBR @ 1-4 water to improve the bond plus seal dusty surfaces
Then silicone or grab adhesive will do the job

Good luck, hope job goes well

 

any kind of hybrid polymer adhesive (stixall, ob1, ct1 ect) would be perfect.