I run Strava on my Pixel 10 Pro Fold running GrapheneOS. IIRC you need to have Google Play Store installed (with zero permissions, preferably) to make Strava work.
You have to give it more permissions. You shouldn't blame GrapheneOS for an app not working when Grapheneos simply gives you more control than stock and you are taking advantage of it.
Of course many apps work fine with turning of more permissions that GrapheneOS allows.