The important detail isn’t which exact term for Jewish scripture will most closely match the old testament in Christianity. The important detail is that “old testament” as a name is meaningless in reference to Jewish scripture, because the term only has meaning if you consider the new testament as equally valid scripture.

So they’re arguing that referring to Moses in a Christian context is “appropriating” Jewish culture, while doing the exact same thing themselves in the exact same comment. If they actually cared at all they’d have known that using any Jewish name for the scripture would’ve served their point better than “old testament”.

As for the Christmas thing, it doesn’t make sense to call a Christmas movie Jewish because if you actually follow Judaism then the birth of Christ isn’t something worth celebrating to you. Any Christ as the savior narrative goes directly against what Judaism believes about Christ. And any Christmas movie without Christ as a savior narrative, might as well be considered non-religious.