Bit late to the party, but I see this question is still unresolved, and I did see a workaround. (found it here: How to link youtube video without captions?)

I noticed when using www.youtube-nocookie.com as base url, the captions do seem to hide in the embed.

Like so: www.youtube-nocookie.com/embed/____the___ID____?cc_load_policy=0&cc_lang_pref=invalid&autoplay=1&modestbranding=1&showinfo=0&controls=0&mute=1&rel=0&loop=1&playlist=____the___ID____

I add the playlist, so I can loop/repeat-1 the movie.