What is the ratio between the electromagnetic force and the gravitational force in the hydrogen atom?

When you are dealing with ratios on the order of $10^{42}$, does it really matter if you use $m_e$ or $M_p$? (on the order of $10^3$)?

The reason to not use proton/anti-proton is two-fold: we don't make bound states of them, and, they interact strongly.

Quarks are even worse, as they don't exist in a free-state. Nevertheless, you could consider the energy required to hold $udd$ together with-in a range of 1.7 fm (the nucleon diameter), and then compare that with the mass of neutron minus the small quark masses.

But this is about gravity, not the strong force. One uses electrons because they are color neutral, and only interact via EM, gravity, and the weak interaction (which is negligible at low energy). You can look at positronium's energy levels and go from there. (You can also compare E and M separately via ortho and para positronium).

It may be more natural to look at the work-horse of bound states: the hydrogen atom, via:

$$ G\frac{m_eM_p}{a_0^2} \ne \frac 1 {4\pi\epsilon_0}\frac{e^2}{a_0^2}$$

where:

$$a_0 = \frac{\hbar}{m_ec\alpha} $$

is the Bohr radius.

Photons don't have mass, so there's no Newtonian gravity, but that is only an approximation. Spacetime curvature ($G_{\mu\nu}$) is due to stress-energy ($T_{\mu\nu}$) and dark energy $(-\Lambda g_{\mu\nu})$. Whether two parallel photons travel in parallel lines would be a good PSE question. Enough photons in a small enough volume yields the kugelblitz black hole, after all.

Regarding the weak force, it could compare $ee$ scattering with $\nu\nu$ scattering. Bound states are discussed here: Can the weak force create a bound state?.

It is indeed difficult to create a formal definition of the relative strength of gravity and EM, as there is no fundamental unit of mass, while the color force is complicated by a lack of free-states, and the strong force is residual. Really only the weak and electromagnetic forces have a formal (energy dependent) relation provided by electroweak unification. The other comparisons are back-of-the-napkin stuff.