You can look here for some ideas:
On this forum I keep hearing things like, “I wore jeans and I didn’t feel out of place” my question is how did the other around you feel? I go to the opera in Budapest once or twice a year and I have asked a few local folks and this is what I have come up with.
Men, sports coat and tie at a minimum. In the boxes go a little more upscale as the boxes are generally Hungarians and for them this is a big deal and you will be mixing with them. If you can’t do this then go to an early performance and sit in the balcony.
If its opening night or something otherwise special; a suit. If it’s a gala, a tux. Even then there were a number that didn’t take that direction: https://1drv.ms/i/s!Ai7Zk-szxfTJg8xLymfSwRH2tWUuLQ I like this photo because I am in it.
The last time we were in the Opera for a typical performance I counted the men that I could see that did not have a coat and tie and the number was 12. Assuming I could only see about half the people and that half those there were men, then the number would be 20 or 30 out of 650.
When booking your tickets be sure you are buying in the Opera House. I heard they were going to close it soon to start a remodel. The second venue is the Erkel theather which isn’t the same thing as being in the opera.
Also don’t overlook the Budapest Operett. Great venue and great shows. Same dress guidelines.
OH, Women's clothes? Anything that looks good in the company of the guy is the best I can do on women's clothing. My wife wears black slacks, shorter heal than most women, a blouse and one of those sequined jackets.....