Hi there! While I have never personally been, I love researching stuff and found this when looking it up.
The biggest thing to remember is that the building is listed as a historical building and therefore the amount of accessibility adaptations they can do is limited. However, they seem to be working on making the facility open for everyone.
If you are going for a guided tour:
The tours are (claimed to be) wheelchair accessible. While no registration is required for individuals, they do ask you come 15 minutes ahead of time. (Groups must register in advance.)
If you are going for a performance:
In total, there are 22 wheelchair accessible seats (all with a seat for a companion) – 4 in the orchestra stalls and 18 more on the balcony. However, these seats are in high demand and must be reserved by directly contacting the opera house directly.
Not all entrances are accessible, but the one at Herbert v Karajan square by Cafe Oper Wien is. Accessible toilets are available and assistance dogs are permitted.
Hope this helps!