Makeup licensing in NC:
https://ij.org/case/north-carolina-makeup-schools/Eyebrow threading in Louisiana: https://ij.org/case/louisiana-threading/
Casket sales in Alabama (after the attention on the case, the AL legislature changed the law): https://ij.org/case/alabama-caskets/
Hair braiding in Iowa (after attention on the case, the governor used line-item veto to remove the offending provisions in a bill): https://ij.org/press-release/victory-african-style-hair-brai...
Hair braiding in Arkansas (after attention on the case, legislators sponsored new legislation to change the treatment of hair braiding under the law): https://ij.org/case/arkansas-hair-braiding/
Hair braiding in Washington (the Department of Licensing changed its rules in response to being sued): https://ij.org/case/washington-african-hair-braiding/
Animal massage therapy in Arizona: https://ij.org/case/azmassage/
Hair braiding in Texas (struck down in Federal court and then fully deregulated by the legislature afterward): https://ij.org/case/txbraiding/
That's the last 5 years or so of won cases just on this issue. They also take on civil asset forfeiture and legislated monopolies (such as taxi companies that have been given an exclusive license to a city), among a few other issues.