Well, those people weren't really "subjugated" before. The only real point of contention there was the language issue, and situation with Russian language in Ukraine is complex - but they're far better off there than, say, English speakers in Quebec.
Basically, the constitution defines Ukrainian as a state language, and Russian as "the protected language of inter-national communication", and it explicitly protects "the freedom to speak Russian". In practice, almost everyone in Eastern Ukraine, and a good part (depending on who you ask, the majority) of central Ukraine actually speak Russian in everyday life, even when they state that their native language is Ukrainian. Almost all newspapers and books are published in Russian. TV news are mostly Ukrainian (but there are Russian channels, too), but most movies are in Russian. Most schools do teach Russian, even those where Ukrainian is a primary education language.
Russian in education is probably the area where most concerns manifest. There are Russian schools, but many argue that there's not enough of them given the number of Russian speakers (but, OTOH, Crimea has barely any Ukrainian schools, despite having 25% of population self-identify as Ukrainian - but Crimea is kinda special, being an autonomous republic with its own unique status). Ditto for Russian universities.
The talk about making Russian the official state language alongside Ukrainian, much like in Ireland or Canada, is occasionally floated, but that would mainly affect businesses (which have to submit tax reports etc in Ukrainian today). In theory, regional governments are supposed to operate in official language, but in practice those in Eastern Ukraine has been using Russian pretty much exclusively anyway...
As for compromise, I think that it was entirely possible before the occupation of Crimea. There were a lot of Russian speakers on Maidan, and that was appreciated - for example, in Lvov, which is considered the heartland and hotbed of western Ukrainian nationalism, they had a "speak Russian for a day" event as a sign of respect, and that was supported by Right Sector and other nationalist groups.
Generally speaking, you should understand that the new government is not actually all that nationalist. The actual nationalist parties are Svoboda and Right Sector. Svoboda has 3 ministers in the new government out of 18, Right Sector has none. Most of the new government is Batkivshchina, which is more pro-Western/European than it is nationalist.
The problem is that the invasion has upset the balance. Basically, the extreme nationalists that claimed that ethnic Russians are the "fifth column" paving the way for Russian occupation of Ukraine can now nod at Crimea as testament to their words. If Russia pushes on, I'm afraid that Ukrainian nationalists will rapidly radicalize, and will start actually persecuting ethnic Russians as intrinsic enemies of their budding nation-state. That region has seen ethnic violence for the sake of nation-building on a large scale before (most recently, Volyn Massacre), so yet another one would be nothing new. And, of course, ethnic Russians in southeastern and central parts would also radicalize in response to that, just as Poles did in Volyn. So this has all chances of blowing up into full-fledged everyone-on-everyone genocide along the same lines as Yugoslavia - assuming, of course, it doesn't blow up even further into a major war between Russia and NATO/EU.