Are Proton and Electron Charges a Coincidence? I was curious why protons and electrons have opposite and equal charges which brought me to this post. Essentially, I was told that there wasn’t really an explanation and that the charges are only confirmed experimentally.
However, this answer left me feeling dissatisfied. I can understand why it may seem like an experiment is only enough. We could say two objects have the same mass and there is no other underlying physics principle to why.
But my question is how do we know for sure that opposite charges aren’t a coincidence? Another post in that thread brought up the fact that opposite charges exist because a proton could theoretically decay to a positron (this can be argued through $\beta^{+}$ decay.) Is there some scientific principle for why the things are the way it is?
And if not, does that mean that it is viable for a world to exist with protons and electrons having unequal or different charges and no physics principle would be changed?
 A: In physics there is nothing that is more fundamental than experiment and observation. That protons and electrons have equal and opposite charge to high precision is known from experiments.
The abstractions of the theory are chosen to match this experimental reality. So, naturally, they appear to "predict" it.
A: A few more points to add to John's answer:

is the fact a proton can decay to a positron a random coincidence or is it due to a more fundamental law of the universe?

The half-life of a (free) proton, by some estimates, is about $10^{34}$ years. That's 10,000,000,000,000,000,000,000,000,000,000,000 years. Some physicists have argued that a proton simply does not decay.

a proton can theoretically decay to a positron.

This idea (free proton decay) was first hypothesized by (I believe) Andrei Sakharov. This has never been observed. In such a mode of decay (or any kind of decay) the product states must be less massive than the initial state(s).
One mode of decay may be $p^+\rightarrow \pi^0 +\beta^+$ but again, this has not been observed even using the most sophisticated experimental techniques and apparatus to date.

it made it seem like opposite charges were more of a coincidence because of one “random” thing protons can do

Whether it's a coincidence or not is irrelevant. The data suggests this is the case, which makes it fundamental in our understanding of particle physics. The way this is worded seems to suggest that free proton decay is something that happens frequently. It never happens at all.

Also, would a world with protons and electrons having different charges be possible? What would it be like?

By different, I assume you mean that electrons and protons would have opposite signed charge? Roughly speaking, the answer would most likely be, no difference, assuming the sign of charge was flipped on every other elementary particle (amongst other things - see CPT invariance which is a fundamental symmetry).
