How do you know that a given reaction is not an acid base reaction? (apart from the fact that it should have an acid and a base and it should be a double displacement reaction)?

Question

I mean I know acids have protons (H+) and bases have hydroxides (OH-) but there are so many other acids and bases that don’t have H+ and OH-.

Answer 1

I think your problem may be that you simply must recognize that there are SEVERAL definitions.
An acid/base pair by the Arrhenius definition may not be an acid/base pair by the Lewis definition which may not be an acid/base pair by the Bronsted-Lowry definition, which may .........and so on into the night. Does this answer your question or have I taken your remarks too literally.
By the way, when I was in school we were taught that all acid base reactions were double displacement and produced a salt + water BUT what about
HCl + NH3 ==> NH4Cl
HCl is an acid and NH3 is a base (both by the Bronsted-Lowery definition) and that's a synthesis reaction.