Understanding how baryonic processes shape the intracluster medium (ICM) is of critical importance to the next generation of galaxy cluster surveys. However, many models of structure formation neglect potentially important physical processes, like anisotropic thermal conduction (ATC). We explore the impact of ATC on the prevalence of cool-cores (CCs) via 12 pairs of magnetohydrodynamical galaxy cluster simulations, using the IllustrisTNG model with and without ATC. Examining their properties we find that the addition of ATC has a negligible impact on the median rotation measure, plasma β, the magnetic field-radial direction angle, and the effective Spitzer value. However, the scatter in the angle and effective Spitzer value is 50 per cent larger with ATC because the magnetic field aligns with the azimuthal direction to a greater extent in relaxed clusters. ATC's impact varies from cluster to cluster and with CC criterion, but its inclusion produces a systematic shift to larger CC fractions at z = 0 for all CC criteria considered. Additionally, the inclusion of ATC flattens the CC fraction redshift evolution, helping to ease the tension with the observed evolution. With ATC, the energy required for the central black hole to self-regulate is reduced by 24 per cent and the gas fraction at 0.01 r_{500} increases by 100 per cent, producing larger CC fractions. ATC makes the ICM unstable to perturbations and the increased efficiency of AGN feedback suggests that its inclusion results in a greater level of mixing in the ICM, demonstrated by the 10 per cent reduction in central metallicity for clusters with ATC.
