Low-temperature (22 K) irradiation with 2.5-MeV electrons, creating point defects affecting elastic scattering, was used to study the competition between stripe C-2 and tetragonal C-4 antiferromagnetic phases which exist in a narrow doping range around x = 0.25 in hole-doped Ba1-xKxFe2As2. In nearby compositions outside of this range, at x = 0.22 and x = 0.19, the temperatures of both the concomitant orthorhombic/stripe antiferromagnetic transition T-C2 and the superconducting transition T-c are monotonically suppressed by added disorder at similar rates of about 0.1 K/mu Omega cm, as revealed through using resistivity variation as an intrinsic measure of scattering rate. In a stark contrast, a rapid suppression of the C-4 phase at the rate of 0.24 K/mu Omega cm is found at x = 0.25. Moreover, this suppression of the C-4 phase is accompanied by unusual disorder-induced stabilization of the C-2 phase, determined by resistivity and specific heat measurements. The rate of the C-4 phase suppression is notably higher than the suppression rate of the spin-vortex phase in the Ni-doped CaKFe4As4 (0.16 K/mu Omega cm).