Charging 12V batteries in series-parallel using a 24V charger

I assume they are lead-acid batteries.

If so, yes, what you are doing will work. Indeed, this is exactly what the industry has been doing for a century.

Despite what others have said, imbalance is not a significant issue with only two 12 V lead acid batteries in series, because at the end of charge the most charged battery will handle a bit of overcharge as the other battery finishes charging.

(Conversely, if these are Li-ion batteries, a whole lot of issues would arise, especially depending on whether or not they are protected batteries.)

Charging and discharging batteries in series can lead to voltage imbalance over time. You can read more about it here. To get the most lifetime from your batteries, you can charge them in series but then you should have a charge balancing circuit.

voltage is doubled when connected in series, but amperage stays the same. When connected in parallel, amperage doubles but voltage stays the same. Wire 2 batteries parallel and then wire the other 2 the same. Then wire one set to the other set in series. Problem solved.