Although this caused a certain coolness with the Austrian royal family, Strauss was by this time too big to fail, and for most Austrians his peccadilloes were probably part of his entertainment value.
It's well-documented that the royal family members are fond of exclusive health retreats. Queen Camilla and King Charles ...
You can also explore the Imperial Apartments (Kaiserappartements) where the royal family lived ... and Prince Eugene of Savoy (who defended Austria from an Ottoman invasion in 1697).