Sure, but the phrase "it's a force with a magnitude that is proportional to the mass" is like me asking "how heavy are you?" and you replying "75 liters", expecting me to know that humans are basically the density of water.

My point is that it really seems like "gravity" is not a force, it's an acceleration, but there is something you could call "force due to gravity" that you reverse-engineer from the known acceleration, and that means you need to multiply by the mass. Clearly different masses will just cancel, so the resulting acceleration is the same.

I'm fine with saying "force due to gravity" or even "gravitational force". Which is what you're describing in your first sentence, and I have no disagreement with that. "Force of gravity" starts to sound a little off, and I bet if I ask "what is gravity at Earth's surface?" I'll get back "9.8 m/s^2", which is an acceleration not a force.