We present a theory for the large suppression of the superfluid density ρs in BaFe2(As1-xPx)2 in the vicinity of a putative spin-density wave quantum critical point at a P doping, x=xc. We argue that the transition becomes weakly first order in the vicinity of xc, and disorder induces puddles of superconducting and antiferromagnetic regions at short length scales; thus, the system becomes an electronic microemulsion. We propose that frustrated Josephson couplings between the superconducting grains suppress ρs. In addition, the presence of "normal" quasiparticles at the interface of the frustrated Josephson junctions will give rise to a highly nontrivial feature in the low-frequency response in a narrow vicinity around xc. We propose a number of experiments to test our theory. © 2015 American Physical Society.