The Free Britney movement has a new fan base on Capitol Hill, as lawmakers with wildly different ideologies work to help a cause once dismissed as niche.

The unusual groundswell began after an appeal in open court last month by 39-year-old pop star Britney Spears, who's fought to exit a legal guardianship she says has prevented her from driving with her boyfriend and forced her to stay on birth control. From Elizabeth Warren to Ted Cruz, prominent politicians are vowing to respond to Spears’ case and reviving a push for...