Somehow I've never heard this song before, or at least at so infrequently that I don't remember hearing it. But I've read about this before so it must have been a point of discussion for a while. Not the type of guy to be excited about Christmas but I like the tune.
As for the controversy itself, it reminds me of The Honeymooners. I've heard a case about Ralph's "one of these days, Alice, bam! Right in the kisser" catchphrase which I think makes sense. It isn't suggesting that he's physically abuse, since "one of these days" implies that he's never actually hit her before. Alice never takes the threat seriously, which suggests that she doesn't believe there to be any actual weight behind it.
But even if the intent was to show that Ralph rather than Alice had the power, it still looks pretty horrendous to have a husband threatening to beat his wife in a comedy, and people might think that the threat is bad enough or that the topic isn't . I can understand that too, so I can't take an issue with people taking either side unless it's coupled with other questionable behaviour, like whining that others have the concern in the first place.
I'm in the same place with this song. I understand the arguments for what the song was intended to be, so okay, I can see how people would take it as an inoffensive song. I can also see how many of the song comes across very poorly anyway, and how at one of its lines sounds a lot worse now because the phrase in it is no longer familiar, and how you might not feel like the woman's unstated intentions justify how the man reacts to what she says. So I can understand why broadcasters might pull the song, even if it's just because they don't feel like it's worth the trouble of having to discuss it. I end up being more concerned with why someone would take a particular stance on this song rather than what the stance they take is.