We discuss whether an unaccounted contribution to the Cosmic Microwave Background polarization $B$-mode by primordial magnetic fields (PMFs) can bias future constraints on inflationary gravitational waves. As a case-study, we consider a scale-invariant PMF spectrum with amplitude of $approx{1},{mathrm{nG}}$ on $1,mathrm{Mpc}$ scales, compatible with current cosmological bounds. We find a degeneracy in the $B$-mode spectra between PMFs and inflationary gravitational waves. If PMFs of this amplitude are not accounted for, future CMB experiments could claim a false detection of a tensor-to-scalar ratio $rapprox 0.007$, close to the predictions of Starobinsky and $alpha$-attractor models. The degeneracy can be broken if $B$-modes are measured also at multipoles $ellgtrsim 900$: more precisely experiments like CMB-S4 or CORE-M5 would be able to discriminate PMFs from primordial GWs at high statistical significance. Experiments like LiteBIRD or PIXIE will not be able to break the degeneracy and will need complementary bounds coming, for example, from measurements of anisotropies in the Faraday rotation angle of CMB polarization. This reinforces the importance of future experimental constraints on PMFs.
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