This is kind of a pain but on the mobile app if you type in a specific song you are looking for and scroll down you'll find multiple listings under the same song name. One of those is the clean versio usually and then you can go from there to the album with the rest of the clean songs. Just discovered this today
I don't think this is a sufficient answer. The new Tribe Called Quest album has both a clean and explicit version on Spotify. I have the clean version saved to my library (which I probably did in desktop), but its impossible to search for it on mobile. It is very frustrating because I want to listen to hip hop around my kids but cant find anything on the go.
You just search for the artist (e.g. Demi Lovato) and then the album after (e.g. Confident). Look for "Albums" and tap "Select All Albums". The clean version should be listed there (along with the explicit version) if the artist released a clean version of the album to Spotify. Artists usually don't release that many clean versions to Spotify like they do for Apple Music.