Oops, easy mistake to make. Don't worry, it's just as easy to fix.
It only takes a couple of steps:
1) On your iPhone, tap the "Settings" icon.
2) In Settings, select "Privacy."
3) In Privacy, select "Contacts."
4) Find the Racefully app in this list, and make sure that the toggle button is green.
And that's it-- you have now granted Racefully access to your contacts. Now it's time to invite a friend!