Public Holiday in Munich?

Corpus Christi is indeed a legal holiday in Bavaria (but not in all German states) and most businesses will be closed. It is a legal holiday in all of Austria and most businesses will be closed. Since I speak German, I checked legal holiday websites for both countries and that's what they said. From my own experience, I remember processions in small catholic towns on this day. If you encounter these, some streets may be closed for traffic.

The German Rail website shows nine trains, five of which are reservable, between 8 AM and noon on June 7. Driving is not normally much faster than the train and on a holiday, the road from Munich to Salzburg might be congested. You won't need a car in Munich when you get there, anyway.

Thanks so much for the information. It seems like we should avoid traveling that day but we would like to get to Munich so that we can fly home the next day.

Why would you avoid traveling that day? The trains will run and you can get reserved seats. No problem with getting to Munich for your flight. With online purchase significantly in advance, you can get tickets, with seat reservations, for a 1½ hr express train from Salzburg to Munich for €29 for two. No worries about crowded trains, no worries about traffic.

If you already have the car, and if you are happy with the drop charge (I'm assuming you have rented the car in a different country) nobody will stop you crossing from Austria into Germany, I'm not sure about the advantage of paying for a rental car day plus train tickets on the same day. If you intend to take the train I would suggest disposing of the car on a previous day and taking the train to and from Hallstatt.

Thanks for the idea. I will indeed look into that because you make a good point about having a car and paying for a train ticket on the same day. I begin to wonder if I should skip the car entirely and do public transportation out of Vienna, to Durstein, Halstatt and eventually Munich.