It should be safe to use the same charger for both battery types.
AGM batteries are usually charged to a peak voltage of 2.4V per cell, which is 28.8V for a 12 cell 24V battery. LiFePO4 cells are fully charged at 3.6V per cell, which for an 8 cell '24V' battery is also 28.8V.
How to charge Lithium Iron Phosphate
A LiFePO4 battery can be safely overcharged to 4.2 volts per cell, but
higher voltages will start to break down the organic electrolytes.
Nevertheless, it is common to charge a 12 volt a 4-cell series pack
with a lead acid battery charger. The maximum voltage of these
chargers, whether AC powered, or using a car's alternator, is 14.4
volts. This works fine, but lead acid chargers will lower their
voltage to 13.8 volts for the float charge, and so will usually
terminate before the LiFe pack is at 100%.
This is not easy as a linear limiter and better with a PWM limiter and LC filter.
If the 12Vaux is fully discharged and requires (14.2-11.2)V*20A=60W series load dump . That is a lot of heat before the Imax reduces to a CV equal voltage to the alternator.
If one considers a light bulb a good solution , this is effectively a PTC almost constant current source when used in the 0 to 10% voltage range defined by DCR which is 10% of rated voltage R. e.g. 12V/20A where filament resistance drops to 10% of DCR at rated voltage at 3200'K Thus 3V*20A=60W , with a DCR of 0.15 ohms then at 10V and 10% DCR the bulb may be something like 30V 1.5Ohms or 45W which is really not a practical value. It might be something like to 12V 70W car headlamps in series/parallel unless you want an AUX light when charging.
So ok in lower currents, but not 20A. This is just a ballpark estimate, not a rigorous calc.
A better solution is PWM with a series choke rated for 20A such as those air coils found in ATX PSU's and a fast switch rate with a MOSFET switch rated for 50A ( hi side or low side. ) THe battery acts as a 10kfarad capacitor with some ESR from 5 mOhm to 1 Ohm when dead. but an RF cap will reduce EMI.
Another way is to just use a fixed 150 mOhm 60W heater wire (NiChrome) and use that to keep your coffee cup warm ;) Or use a Cap Pulse discharger rated for high RMS ripple current ( several large plastic caps in parallel) This is essentially an active SMPS current limiter with a 0.1V max drop at CV mode at 14.2V or 0.1V/20A = 5 milliohm (MOSFET + choke DCR)
I said to do this right is not easy and stay within limits.
Ultimately the simplest solution is get a bigger battery rated for the current of the alternator, but then you may end up blowing your Alternator diode bridge with both batteries are weak and drawing max current of alternator for long periods at 180'C junction temp.
You can look at NTC disc surge limiters, but they cannot protect a battery as they are designed to protect perhaps only 0.5Farad and not a battery with 10k~100K Farads. To understand read , https://www.digikey.com/en/ptm/a/amphenol-advanced-sensors/cl-series-inrush-current-limiters/tutorial. To dump 40 Watts of heat it either has to run extremely hot or be big like headlamp bulbs ( which will get hot and must be sealed from moisture).
Best Answer
A simple supply is not a good choice for charging liFePO4 batteries for a number of reasons.
Initially when charging LFP you supply it with current and the battery will decide what the voltage is. Practically for you this means that you need a supply that can provide a constant current to the battery. You say that you assume your supply will shut off at 20A. Assuming anything around these batteries can be a very expensive mistake and this does not give you a constant current source.
When the battery reaches the bulk voltage limit at 13.8V you need to let the battery absorb at that voltage until the current drops to C/20 (that would be 5A for a 100AH battery), and then STOP CHARGING. You can ruin your batteries by allowing them to float with a 13.8 charge voltage. Your BMS will not protect you against that.
I know links are frowned upon but there is a lot of good information on Nordkyn design's website.