I actually feel little sad about how overly careful people have become about holiday greetings. For me it does not matter if I don’t celebrate it (and let’s be honest, I rarely celebrate the ones that are part of my culture), I just enjoy hearing and learning about things other celebrates.
I would say that the card itself is not the issue, but what you write on it. Telling about the occasion and sharing what you did / are planning to do on the day is great, but writing as you assume the recipient celebrates same holiday or making it too religious can give rude vibes. But then again I have been wished happy 4th of July and the only result was deep confusion because I had no idea then when is so special about 4th of July (I went on for months thinking they are just very positive person who enjoys wishing happy day for people in their own day and I am little ashamed about how long it took me to understand). The only time I have been (slightly) offended about anything holiday related on Postcrossing was when somebody mentioned how sorry they feel for me as they believed there are no holidays for me between autumn and Christmas. Finnish independent day is 6th of December and we have a week long school break in autumn so I was little annoyed, but we got that misunderstanding quickly solved.
So I would say that holiday cards are all okay so long the profile does not specifically say that they do not want those. Also, I would love people to be more brave about sharing their celebrations!
I wouldn’t mind at all if I received Thanksgiving card so long you wrote something about what you are doing then. We already know Thanksgiving, thanks to all the numerous American TV-shows, but most of us know it only as it is shown on TV…
I might be mistaken, but I have understood “happy yule” is used mostly by those who follow paganism, and “happy holidays” is the (un)official neutral version. I usually go with happy holidays since it could refer either to Christmas or New Year or anything else celebrated around that time.