Would dipping meat in vinegar break the protein bonds in the meat? Making the meat have less protein content?

Since it is acetic acid.

Like, dip it (the meat) in a vinegar solution with chili in it, before eating it.

Yes many acids will break proteins up into smaller peptides or proteins and thus "tenderise" meat. That should not however reduce the protein content.

Just to add to this, table vinegar is generally a very low concentration of acetic acid at around 5%. At this level, it is mostly harmless other than being rather irritating - acetic acid is an irritant to the mucal membrane*. At higher concentrations, acetic acid can cause skin burns and permanent eye damage.

In studies where it is necessary to dissolve connective tissues to dissect out individual muscle fibers, the common agent used is nitric acid, which is highly corrosive and very dangerous. In such studies, concentrations of about 15~30% is generally preferred. Still, it takes hours for connective tissues to dissolve. An alternative will be to simmer the meat in sulpheric acid which is slightly safer and takes less time. So if you were to use table vinegar for this, it would take quite a bit of time...

* I had the misfortune of accidentally sniffing in residual acetic acid fumes once - fortunately though, it did no damage to me as my friend had already gotten rid of the liquid and had been trying to volatize any residues with a hairdryer, which works fine with alcohols and ethers but not acetic acid...that's why one should pay attention to what your teaching assistants say during lab practicals!