I feel a duty to correct Tim (mandatory xkcd: https://xkcd.com/386/) ;-).
Equating "vor" with "for" is not quite correct. The two share a (proto-)Germanic root *fur but vor/fore separated at least half a millenium ago from für/for.
The Latin equivalent of für/for is pro: für umsonst1 = Pro bono = for the good [free of charge], fürs Vaterland = pro patria = for the fatherland.
The Latin equivalent of vor/fore is pr[a]e: Vormann = foreman ~ praetor, voraussehen = foresee ~ predict, etc. The meaning of of this word group is "before", in a spatial, temporal or metaphorical, e.g. social, sense.
The German prefix vor- is very frequent; here is a long list. Some have a similar meaning as vormachen: vorschützen, vorgeben, vorspiegeln, vorspielen or vortäuschen; vorlügen is a reinforcement bordering on a pleonasm, but emphasizing the "performative aspect", if you want.
Getting back to the original question: My entirely unsourced native speaker intuition interprets the semantics of vormachen as "performing something in front of the actual situation". It is obscuring the facts behind it, almost a theater piece. A facade, like a Potemkin village. Der Zarin wurde etwas vorgemacht.
By contrast, für/for/pro indicate a direction or goal (of intent, of an action) which sometimes can be mutual, forming an equivalence (stand in for someone, tit for tat). While there is a common root with "before", which apparently lasted longer in English than the German für/vor connection, the meaning is now quite different.
1That's grammatically borderline wrong, very casual German, but for bad German it's quite idiomatic and a nice example.