Who's ever had any issues with the Greek ladies wearing their tiaras?
I don't see any issue here. Anyone who owns a tiara can wear it when appropriate. There is no rule that only aristocrats or royals can wear tiaras.
Besides, why wouldn't the ladies of the former Greek royal family wear their family jewels and heirloms? That has nothing to do with their citizenship status or their allegiance to the Hellenic Republic.
A more sensitive issue in my opinion is whether they will keep wearing the Greek dynastic orders or not. I am not sure, but I assume it might be illegal to do so in Greece. That wouldn't prevent them from wearing them outside Greece (for example, when they are invited to white-tie galas in foreign countries), but I suppose that could be interpreted as a violation of the oath they took when they became Greek citizens, or maybe not (it is controversial to say the least).
The agnatic descendants of King Victor Emmanuel III for example had to swear allegiance to the Italian Republic to be allowed to return from exile to Italy, but they keep wearing and granting the Savoy dynastic orders. The Savoy orders are, however, a corporation with its seat, I think, in Switzerland (?). It is in fact the Savoy family's business and they make money out of it. Wearing the orders in Italy itself is theoretically forbidden, but that doesn't seem to be strictly enforced (again, I am not sure). The Savoys definitely wear them outside of Italy to say the least.
Edit - what the deal with their Danish side. Do they have royal titles from being grandchildren of a Danish King? So even if they renounce Greek titles are they keeping Danish ones?
I am not sure.
The common claim
used to be that all
male-line descendants of King Christian IX had the title of
Prins/Prinsesse af Danmark, but all descendants of Christian X (both in paternal or maternal line) who were in the line of succession under the Act of Succession of 1953 had the title instead of
Prins/Prinsesse til Danmark. However, at least the latter has been now contradicted by the fact that Prince Joachim's children, who are descendants in maternal line of Christian X and are in the line of succession to the Danish throne, have been nonetheless stripped of the title of
Prins/Prinsesse til Danmark and are now only
Greve/Komtesse af Monpezat, which is a title in the Danish nobility, rather than a royal title.
If Joachim's children are no longer princes/princesses, despite being successors to the Danish throne, it would be illogical in my opinion for King Constantine's descendants, who are
not in the Danish line of succession, to be considered Danish princes/princesses, even though they are male-line descendants of Christian IX.
But, again, I am not sure. Maybe the Danish members can clarify.