How does the Higgs Field distribute mass to particles? I am aware that it is through distributing weak hypercharge but am confused as to what distinguishes a photon and an electron to the Higgs Field. Both possess spin and the capability to travel at light speed yet somehow only an electron is given mass and effected by this field. So in total how does the Higgs Field decide what to interact with or what keeps the Higgs Field from interacting with photons per se or other massless particles?
what keeps the Higgs Field from interacting with photons per se
In the electroweak theory, the B boson (the gauge quanta of the U(1) weak hypercharge interaction), and the W bosons (the three gauge quanta of the SU(2) weak isospin interaction) do interact with the Higgs vacuum condensate.
However, there is specific combination of the B boson and neutral W boson that propagates freely in the condensate; this combination is the physical (observable) photon.
See, for example, the relevant Wikipedia section of the the "Higgs mechanism" article
This combination of generators (a z rotation in the SU(2) and a simultaneous U(1) rotation by half the angle) preserves the vacuum, and defines the unbroken gauge group in the standard model, namely the electric charge group. The part of the gauge field in this direction stays massless, and amounts to the physical photon.