The water softener cartridge shown on the autogeek website appears to be a Pentek WS-10 cartridge or clone. The WS-10 has a recommended flow rate of 0.5 gpm. According to its pressure drop versus flow rate curve, the pressure drop at that flow is less than 2 psi. The graph shows a maximum flow of 1.5 gpm, where the pressure drop is about 5.5 psi. The recommended flow rate for the cartridge isn't based so much on flow rate but on softening. There is so little resin in the cartridge that higher flows will cause some hardness to pass through.
The real issue will be the capacity, which is rated at 750 grains. Hardness is considered "high" at 10 grains per gallon (gpd). At that level, the cartridge is rated to soften only 75 gallons. At 25 gpg, it will soften only 30 gallons, probably not enough to last a weekend.