I think the situation is similar to the fact that Crown Princess Margarita is successor to the throne even though the current constitution does not allow it as previously discussed. As far as the King is concerned, he has removed Irina from the succession as per the website, but there is no legality in it as such. I THINK I've got this right but someone more clever than me may be able to confirm!
The situation is more complicated than that.
The current constitution of Romania establishes Romania as a republic. Therefore the government of Romania technically has no power to change the succession or to approve the changes to the succession, because they can't do so within their constitution.
However, the Romanian Royal Family's succession was governed by the constitution prior to the fall of the monarchy. Which means that in order for Michael's changes to be valid the government has to approve them - but would be operating with a no longer valid constitution.
It reasons that if the RRF were restored during Michael's lifetime then the succession that he's operating under - with Margarita being the heir presumptive, and Irina and her descendants being excluded - will be put into place, with Salic law and equal marriage requirements being abolished, and either male preference or equal primogeniture being established, as well as rules regarding the stripping of an individual's titles and succession rights.
If Michael dies without a restoration then it remains to be seen what kind of support his heirs will receive from the monarchists of Romania - if Nicholas and the monarchists support Margarita then I think Michael's wishes will continue to be reflected in the future, but if there's division within the family or the monarchists then what's being done now could fall apart.
Personally, I hope they remain a united front, because I think that's the best chance of a restoration (if the Romanians want it). If you look at Russia, the thing that really kills the chances of a restoration there is the fact that the people don't know who should be the Tsar in the event of a restoration. Without that clarity the monarchy is screwed.