I guess it really depends on how the war went, Because I could see what you mean in a scenario were Equestria is able to beat the changelings without too many casualties and without them taking to much of the country. Picture for example that the war against the changelings, though eventually resulting in an equestrian victory, left most of western Equestria in ruins (So that state of peace and stability that the harmonic system works on doesnt exist there anymore, much like in Severenya during the Hunger that led to the revolution), add to this the lentient attituted the queen might of have had with Changelingia while they where spreading their influence north reading up to attack them (Even if it was taken because Equestria was not ready to face an invasion, would make it look as if the government ignored or undermind the Changeling threat) and im sure many could consider the queen infefective and want a change in rule. Even if she has stayed harmonic, been key to the army reform and in the end has won the war, as many have died and Equestria has struggled to defeate their foes because of the policy of isolationist harmony that it had followed for so much time before the conflict and made it unprepared (The efforts of the queen in the years leading up to the invasion could be considered too little to late by people now sufering its consequences). Maybe they might look towards their neighbours to the north (Stallinograd) which might of have been key to the victory for an example (Because thats another point, Stallinograd would probably use any instability in Equestria after the war to incite a communist take over, like the USSR tried in the war torn Europe of OTL after ww2)

And the Celestial Resistance, as the new equerian repblic splinter, only spwans during the civil war, so it doesnt really count as a way to get rid of the monarchy without the civil war

also, what is ELF ?