Actually mixing batteries can hurt.What kind of battery is the stinger?
If the Red Top and Stinger are both AGM types, then you are OK.
If you mix different types of batteries like a Gel Cel oe Wet Cell connected to and AGM, you will wear the batteries life down faster.
The reason is becasue of unstable voltage and varying charge rates. The batteries will actuallly charge eachother and the plates will heat up. If the batteries sit at different voltages (one at 12.5 and another at 12.9) Then current will flow from the higher battery.