This has also happened to me for a client's site! I'm not even using custom fonts on this site. I can see all the correct fonts in editing mode but the live mode suddenly changed last week all to Times. I removed the (very limited) custom CSS, cleared my cache, opened it in an incognito window. I've scrubbed the backend for any additional coding the client might have put in (she didn't but I wanted to double check).
I am stumped. I don't know what to do or how to make the live site reflect the original design. It looks terrible with Times all over the site.
Can anyone help?
https://www.abovebeyondweddingdesigns.com/