Toddler touching herself

I know this is normal toddler behavior but my daughter keeps touching herself and won’t listen to us telling her it’s a private activity. She’s two months shy of being 3. We tell her she can do it in her room but that it is a private activity so she should do it in her room. We also remind her that mama and papa don’t do that in public and her teachers don’t either. We haven’t gotten mad at her or raised our voices (we generally take a gentle parenting approach). But she’s not listening to us and keeps on doing it all over the house. She’s also taken to taking all her clothes off which has increased how often she’s been doing it (she’s learning how to dress/undress herself right now and I also think she just likes being naked - which is fine).

The reason I want her to stop is I am worried she is doing this at school and when she has babysitters (which are family members who may be more uncomfortable with her doing this so much). I am also wanting her to stop because she has dirty fingers and I don’t want her to get some kind of infection. Tips on how to get kids to do this in their room? Or how long did this phase last for others?