Their situation is completely bizarre. They act and behave in many ways as reigning royals, except that they aren't. And the Romanian Republic seems to sanction it.
They make excellent use of this. They could have stayed in Aubonne, Switzerland, waiting for another 100 years if Romania possibly, possibly, possibly
ever will restore the monarchy.
That will
never happen and they have carved out a total new phenomenon: a functioning Royal House in the framework of a republic. This is not completely unique: between 1588 and 1795 there was an acting Royal House in what was euphemistically called a "Republic" in the Netherlands.
Imagine that Austria or Portugal grant a similar semi-official status to Karl von Habsburg respectively Duarte Pio de Bragança. That the immense role of their Houses in the histories of Austria resp. Portugal is acknowledged and that there is a role in the State's ceremonial and protocol, there is really little harm in that.
I find the Romanian well-willing grace and favour towards the former royal family a great example. Even more: might any monarchy be ended in the Netherlands, Sweden, Spain, whatever: most likely these will fall after democratic referendums and not by revolutions. Hopefully the new republics will be as gracious as Romania and acknowledge what the diverse royal families have meant in centuries of shared history and offer a similar arrangement to the Orange-Nassaus, the Borbóns, the Bernadottes, whatever.