I have a solid-state PWM charge controller with a regulation voltage of 14.1 V. Can I safely use this to keep a 12 V 50 Ah LiFePO4 battery charged? I understand that the PWM controller is less efficient, but I'm not concerned with efficiency. I'm looking for a reliable setup. From my reading, the battery will never fully charge to 100% but by keeping volts at 14.1 the battery BMS won't shunt the current?
Yes, that will work.
But keeping a LFP cell at 3.525 V will over time degrade it (mostly increase its internal resistance. If you could lower that to 3.4 V / cell (13.6 V for the 4 cells in series), or, better yet, stop charging when the battery is full, that would be better.