If a lithium (LiFePO4) battery has a built-in BMS, why does the battery charger have to have a lithium setting?

The BMS in the lithium battery is for the battery protection of low voltage cut out, excess current turn off, over charging protection. It is mainly for preservation, not charge management.
For a 100 Ah battery, it will also limit the battery output to 100 amps (Max) and will shut down with a short of up to 350A for 3 seconds. Below 10V the BMS will turn off and no voltage will be seen at the battery until a wake-up source is put onto the battery.

Here are the recommended charger requirements for BMPRO Invicta lithium battery:
Charging A standard Constant Voltage (Automatic) SLA Battery charger can be used to charge BMPRO Invicta Lithium batteries, however the following requirements must be met:
• Charger must not contain Sulphation/Equalisation setting. If so then this step needs to be turned off.
• Maximum charge voltage of 14.6V
• Recommended float charge voltage 13.9 +/- 0.1V.

The solar and DC-DC may be suitable if they can achieve the specified voltages as long as they don’t have the sulphation and equalization.
If they only charge to a lower voltage, they may work but not fully charge the battery.