Wagner has something of an association with Nazism for a number of reasons, including of course Hitler's praise for him, the ties of his children with the party which of course directly intertwined them, not to mention his own anti-Semitism. Rightly or wrongly, the association was (and is) very much 'a thing'. It reminds me somewhat of the similar association with Nietzsche, which is generally pushed back against now, but at least in the immediate aftermath of World War II, saw a serious slight against him as "a Nazi philosopher". As such it lead me to wonder whether Wagner suffered a similar repudiation for a time, and more generally how this connection played out with his legacy in the years since the war.
It doesn’t cover your whole question, but you’ve reminded me of an old answer by u/caffarelli on the American popularity of German opera during and after WWII.
/u/caffarelli's post sums it up pretty well. There was no real pushback against the music of Wagner after the war. However more recently there's been more of a critical lens put up to operas in a modern context. Operas like Madama Butterfly and Turandot are being criticized for being Orientalist and played in "Yellowface" ( https://www.chicagoreader.com/chicago/turandot-lyric-opera-puccini-orientalism-yellowface/Content?oid=36522180 ) , Othello is only recently not being played in blackface: https://www.theguardian.com/music/2015/sep/22/otello-metropolitan-opera-scraps-blackface. Likewise there's cultural criticism against Wagner's music promoting anti-semitism. Radio stations and performers in Israel don't play Wagner (not by law, it's just heavily frowned upon): https://www.france24.com/en/20180903-israeli-radio-apologises-after-playing-music-anti-semitic-wagner . Although there are Jewish conductors who are known to program his works regularly, even now: http://www.bbc.com/culture/story/20130509-is-wagners-nazi-stigma-fair .
So, it's not banned, but it's... loaded, shall we say. In the past few decades, we've become more aware of the problems with the drama, storytelling, and casting with operas, and there's a lot more discussion being had about if these works should be performed at all, performed with a more culturally sensitive lens, or whether an exception should be made because it's "art" or "tradition". And Wagner is being discussed in the same way. That being said, there's been no shortage of Wagner performances since WWII (outside of Israel), and more and more companies are starting to take on monumental productions like the entire Ring Cycle, but the discussions around it are growing, including discussions of the characters that are obvious anti-semitic stereotypes.