As a physicist who has taught at university, one of the things I most hope to do with my students is to get them to begin to ask questions. The physical universe is like a big machine and it is one of the delights and privileges of the practicing physicist to try and unravel the inner workings of that machine. The only way to do this is to investigate questions. When a student begins to ask probing questions, those questions will usually appear odd. Thus, for example, one has the title question, "Could protons be 're-formed' anti-electrons?" Key in such situations is to encourage the questioning and indeed such speculation while yet being respectful enough to give a real answer to the question. Every scientists I have known who has come up with a genuinely useful new idea started by treating "odd-ball" ideas. This is comparable to the fact that a child does not begin to run before having learned to walk.
So what of the title question itself?
At first glance, one may wonder if, as the title of this discussion suggests, positrons [i.e., "anti-electrons"] might not just be another form of a proton or vice-versa. After all, both are sub-atomic field/particles with charge +e. So why can these particles NOT be identified with each other?
The answer lies in other properties that these field/particles possess. First, the mass of the positron is identically that of the electron [0.511 MeV/c^2- a tiny value] while the mass of the proton is [938 MeV/c^2] over a thousand times more! Second, the positron does not interact by the strong nuclear force, but the proton does.
Related to this latter point is that a proton has an internal structure; it is made up of two up-quarks and a down-quark. [The names of these quarks started as a physicists' joke but they stuck.] One can tell this by its scattering properties. By contrast, a positron has no internal structure; it is not made up of quarks or anything else.
Finally, a positron is an anti-lepton and a proton is a baryon. These are separate classes of particles with very different physical quantum numbers which govern the types of interactions these particles can have with other field/particles. A positron has lepton number -1 and baryon number 0, while a proton has lepton number 0 and baryon number 1. In any interaction, the total baryon number and total lepton number cannot change or the reaction is just as physically excluded as if the energy were to change.
In short, the answer to the title question is decidedly, "No," but one only comes to understand the physical world by addressing such questions.