Italicization of mathematical symbols: quantity symbols vs units symbols
The general approach (see e.g. NIST or IUPAC for sources) is to consider physical constants, such as the proton mass, as quantities. They are thus usually italicized, even when used as units.

Certain units, notably the electronvolt (eV) and the atomic mass unit (u), are considered so important that they are "accepted for use with the SI system", see the SI brochure. These should be given in roman type.