Not entirely true, the monarchy favored the CP but the political elite favored the Entente and you can tell which one won the struggle.Re: Romania
IIRC, didn't Romania tend to prefer the Austro-Hungarians as partners to the Russians up until the Russians promised them Transylvania to join the war (and promptly caused the country to be largely occupied)? IIRC the Romanians had some... pretty severe issues with Russia regarding not just Bessarabia, but also the actions of the Russians while the Principalities were under their "protection" some decades earlier.
While some irredentist elements in Romania will try to cause trouble, it's likely that the situation will have the Russians being even more reviled there, not only did they screw over the country while it was a protectorate and steal half of Moldavia, but they also tricked Romania into a war they could not win, and the only good thing that came out of it (annexing Bessarabia) was something that they could have done without even entering the war (hindsight, of course, is 20/20, no one expected Russia to collapse so spectacularly), not to mention, Romania lost a good chunk of its gold reserves that were "for safekeeping" in St. Petersburg when the October Revolution happened. (Unless that has changed? But I think the POD is at least after the reserves were sent to St. Petersburg)
So I think it's likelier you would the see the monarchy use the anti Russian sentiment as a tool against their political enemies for popular support and the elite to largely favor besides wanting a another war use of the current Russian situation as a way to be A useful to their Entente backers and B as a tool of negotiations for pressure on the central powers.
Sides that, you've also got the issue of AH Romanian Volunteer Corps in Russia which is made of traitors to empire which could be a issue, though settling them in Bessarabia and Romania shutting up about their claims I can imagine being good for AH given their issues with frankly a lot of their ethnic issues and the need to protect the eastern part of the state (Poles, Ukrainians, Serbs, Slavs, Romanians really the post war legacy for what happens in the empire will interesting in both dealing with traitor/insurgents but also preventing new uprising/revolts).
Greece has a similar situation where the king favored the CP and elite Entente and with the enemies backing a war they lost their positions are strengthened.