I believe that there’s some app out there for Android that lets one create a spoofed environment for apps that demand certain permissions to function. Returns bogus data to them. Might require a rooted device, though.

goes looking

Yeah.

I think I’m thinking of XPrivacyLua, which requires Xposed, which in turn requires a rooted device.

EDIT: all that being said, I do think that if practicable, it is kind of an argument to use something other than Instagram, and more broadly, to try to keep use on a personal computer rather than phone, where it’s easier to deal with or avoid shennanigans like this.