  Gravitational-wave astronomy, together with precise pulsar timing and long
baseline interferometry, is changing our ability to perform tests of
fundamental physics with astrophysical observations. Some of these tests are
based on electromagnetic probes or electrically charged bodies, and assume an
empty universe. However, the cosmos is filled with plasma, a dilute medium
which prevents the propagation of low-frequency, small-amplitude
electromagnetic waves. We show that the plasma hinders our ability to perform
some strong-field gravity tests, in particular: (i)~nonlinear plasma effects
dramatically quench plasma-driven superradiant instabilities; (ii)~the
contribution of electromagnetic emission to the inspiral of charged black hole
binaries is strongly suppressed; (iii)~electromagnetic-driven secondary modes,
although present in the spectrum of charged black holes, are excited to
negligible amplitude in the gravitational-wave ringdown signal. The last two
effects are relevant also in the case of massive fields that propagate in
vacuum and can jeopardize tests of modified theories of gravity containing
massive degrees of freedom.
