You said it yourself, their government is illegimate and there is a great deal of sympathy for the monarchy in general and the Hapsburgs in particular among the people of Austria. Revolutionary governments can't tolerate those threats to their regime.
In this they are just the same as the Italians (not that I would ever shed too many tears over the misfortunes of the Savoias) who expelled their royals for not stopping Mussolini from taking power (guess they should ignored the voice of the people, huh) and yet at the same time have allowed Il Duce's own granddaughter Alessandra Mussolini to serve in the Italian government.
-Not that I'm completely against Alessandra Mussolini, her opposition to the EU and increased Muslim immigration both have my sympathy.