If you insist on treating revenue sports as just another extracurricular activity, then be consistent.
A music major on scholarship, who also participates in a univeristy sanctioned glee club faces no prohibition, from either their scholarship or their extracurricular participation, against using their musical talents to earn money outside of their school or extracurricular activities. They can earn money performing, selling their music, or using their music to market products on social media. If NCAA athletics are just another extracurricular activity, why should the rules be different?