  We study distribution dependent stochastic differential equations with
irregular, possibly distributional drift, driven by an additive fractional
Brownian motion of Hurst parameter $H\in (0,1)$. We establish strong
well-posedness under a variety of assumptions on the drift; these include the
choice $$B(\cdot,\mu) = f\ast\mu(\cdot) + g(\cdot),\quad f,g\in
B^\alpha_{\infty,\infty}, \quad \alpha>1-1/2H,$$ thus extending the results by
Catellier and Gubinelli [9] to the distribution dependent case. The proofs rely
on some novel stability estimates for singular SDEs driven by fractional
Brownian motion and the use of Wasserstein distances.
