  Transmission spectra are differential measurements that utilize stellar
illumination to probe transiting exoplanet atmospheres. Any spectral difference
between the illuminating light source and the disk-integrated stellar spectrum
due to starspots and faculae will be imprinted in the observed transmission
spectrum. However, few constraints exist for the extent of photospheric
heterogeneities in M dwarfs. Here, we model spot and faculae covering fractions
consistent with observed photometric variabilities for M dwarfs and the
associated 0.3-5.5 $\mu$m stellar contamination spectra. We find that large
ranges of spot and faculae covering fractions are consistent with observations
and corrections assuming a linear relation between variability amplitude and
covering fractions generally underestimate the stellar contamination. Using
realistic estimates for spot and faculae covering fractions, we find stellar
contamination can be more than $10 \times$ larger than transit depth changes
expected for atmospheric features in rocky exoplanets. We also find that
stellar spectral contamination can lead to systematic errors in radius and
therefore the derived density of small planets. In the case of the TRAPPIST-1
system, we show that TRAPPIST-1's rotational variability is consistent with
spot covering fractions $f_{spot} = 8^{+18}_{-7}\%$ and faculae covering
fractions $f_{fac} = 54^{+16}_{-46}\%$. The associated stellar contamination
signals alter transit depths of the TRAPPIST-1 planets at wavelengths of
interest for planetary atmospheric species by roughly 1-15 $\times$ the
strength of planetary features, significantly complicating $JWST$ follow-up
observations of this system. Similarly, we find stellar contamination can lead
to underestimates of bulk densities of the TRAPPIST-1 planets of $\Delta(\rho)
= -3^{+3}_{-8} \%$, thus leading to overestimates of their volatile contents.
