High-test hydrogen peroxide (HTP) can be stored at room temperature, but is not long-term stable. Decomposition of hydrogen peroxide is what limits the Soyuz to a bit over 6 months of operating lifetime. HTP/kerosene has a lower specific impulse to begin with, and its performance will be even lower by the time the craft reaches Mars due to decomposition of the oxidizer.
Maintaining even that low of a decomposition rate requires extreme care to avoid contaminating the tanks, plumbing, or peroxide oxidizer. In LEO, discovering unexpectedly high decomposition might mean coming home early, for a Mars mission it would mean not having enough performance left to land. The hazard isn't limited to reduced performance either, HTP is capable of runaway thermal decomposition and its vapors can decompose explosively. On contact with some substances, it can cause serious corrosion or even spontaneous ignition.
LOX and LCH4, if you have active cooling systems, can be stored indefinitely, without many of the hazards of HTP. They can also be produced on Mars from local materials. If you don't have active cooling or a mass budget for passive storage of cryogenic propellant, more traditional hypergolic systems have better long-term stability.