It may or may not take a client restart on your or their part (or both as it probably involves some work on the backend) but it definitely is the case. It’s been that way for a few years now. As I mentioned it’s character specific. If you ignore them on your DK and the next day you’re on your Hunter they’ll be able to message you again on that character but won’t as soon as you hop back onto your DK.
It’s never been officially acknowledge and I checked WoWpedia and it has sparse info but if you search it up you can find all kinds of threads on the matter.
I had a spat with someone once and later on an alt they didn’t know about went to trade them some items I had mentioned giving them but I guess they were still sore as it said “this person is ignoring you” and I couldn’t open trade. You should be able to test it with a friend by having them ignore a character of yours. Both restart the game and any bnet clients (just to be safe) then try messaging them on an alt on that character of theirs that ignored yours. Shouldn’t work.
Edit: Found an actual blizzard resource stating that ignores are account-wide: Spotlight on: Harassment