After all, what is the theme of Cinderella? Never giving up? Justice will "out" in the end? Whatever you think the theme is, you can use that for your stories.
Themes such as anti-bullying emerge from stories like The Ugly Duckling. (Also beauty is only skin deep and transformation is always possible! Lots of themes from this one).
The lovely thing is that the themes from fairytales are timeless. It is one major reason we still love these old stories. They still resonate. I think they always will. They reflect on our nature. There will always be jealousy (Snow White), a need for sensible building materials (The Three Little Pigs!), and greed (Goldilocks - I always have sympathised with the three bears here). That is to name just a few examples.
And there's nothing to stop you combining themes either. After all your lead character may have the virtues of, say, Puss in Boots and the villain the qualities of The Big Bad Wolf. Set up the conflict and away you go!