Gravitational-wave (GW) 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 (EM) 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 EM 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 super-radiant instabilities; (ii) the contribution of EM emission to the inspiral of charged black-hole binaries is strongly suppressed; (iii) EM-driven secondary modes, although present in the spectrum of charged black holes, are excited to negligible amplitude in the GW 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.