There is some evidence of fine tuning in the properties of various elementary particles and atomic nuclei, but there are lots of different ways that complicated structures can emerge, so it may be difficult to argue absolute fine tuning.
For atoms and molecules, we don't depend on having a precise value of the fine structure constant, only on having a value that's much less than 1. In fact, atomic and molecular structure is largely derived from electrons having spin 1/2 and thus being fermions. Nuclei also enter into that structure, but only as tiny opposite-charged objects much more massive than electrons.
It's hadrons and nuclei where we see the real fine tuning.
First, hadrons. The are only two long-lived ones, protons and neutrons, or collectively, nucleons. They are very close in mass because the up and down quarks are much less massive than the color-confinement energy scale. Color confinement forces these quarks to be in a much smaller size (about 10^(-15) m) than their Compton wavelengths (about 10^(-13) m). If one works out a "bag model" approximation, where quarks with mass m are confined within a radius R, then their energy is
E = ()/R + ()*m + ...
This is from quarks having Dirac wavefunctions -- that's why we don't get ()*m^2/R + ...
The ()'s are quantities that are approximately 1, quantities that I won't go through the trouble to calculate here.
The electromagnetic self-energy is ()*alpha/R.
At least in the electrostatic limit, the electromagnetic self-energy is larger for protons than for neutrons. But neutrons are more massive than protons. That implies that the down quark is more massive than the up quark, and odd circumstance. For the other quarks, it's the reverse: the charm quark is more massive than the strange quark, and the top quark more massive than the bottom quark.
If the color-confinement energy is much less than the mass of the least massive quark, then the lowest-energy state will be three quarks with that flavor with spins aligned, making total spin 3/2. The next states up in energy will be excited states of that system. It may make "molecules", but I'm not sure about that.
String theory yields the Standard Model by symmetry breaking, but that symmetry breaking is a function of the space-time topology. Different topologies will yield different low-energy limits, and assessing the habitability of universes with these various limits will be *very* difficult. So I'm not going to get into that aspect of the problem.