Evaluate whether the Crimean War was a liberal or conservative reaction to the events after the Congress of Vienna and the Revolutions of 1848.

In my opinion, we can see the Crimean War, somewhat paradoxically, as a manifestation of both liberal and conservative thinking on the part of the European countries that waged it.
After the defeat of Napoleon, the European powers made an effort at the Congress of Vienna to turn back the clock and restore the status quo ante bellum to the extent they could. The monarchy was restored in France and the German states, though the Holy Roman Empire could not be resurrected, it was reconfigured as the German Confederation. A new situation in 1815, however, was that Russia had become a major European power and began to be seen by the governments of Britain and France as a new threat to the stability of Europe, in spite of Russia's huge role in Napoleon's defeat. The Revolutions of 1848, though not resulting in territorial changes, intensified the reactionary stance of Europe's ruling class. When Russia again flexed its muscles in the East, presumably to defend the Christian minorities in the Ottoman Empire but perhaps mainly to increase its own power, Britain and France saw this as an intensification of the threat they already believed the upstart Russians were causing to the stability of Europe. So, in a somewhat ironic twist, the British and French, who less than thirty years earlier had helped the Greeks win their independence from the Ottoman state, now sided with the Ottoman Empire against the Russians. They did not do this simply out of an abstract fear of Russian expansionism. The Russians were primed to destabilize the Balkan countries (which later became Yugoslavia) in order to help their fellow Eastern Orthodox ethnic groups there, and it was feared that the independence of these smaller nations, such as the Serbs, would have a spillover effect elsewhere in Europe. Also, the British, especially, wanted to insure their own control over the trade routes to India, which would be threatened if the Russians took over Ottoman territory in the Middle East. The declining Ottoman state was already heavily controlled by the British, and the Russians were a threat to that control. Therefore the British, and their French allies, fought in the Crimean War to defend the Ottoman regime, and this was a conservative maneuver to maintain the existing stability of Britain, its colonial empire, and all of Western and Central Europe.
From the Russian side, however, one could interpret the war as a sign of liberal thinking. The Russian elite wanted to expand the power and territory of Russia, but there was also a genuine desire to liberate the European peoples who still were subjects of the Ottoman Empire, for humanitarian reasons as well as conservative religious ones. And even on the British and French side, there were liberal elements that were opposed to Russia not simply to protect their own interests, but because Russia was considered a backwards, authoritarian country, still at that time having serfdom, and with a leader, the Czar, who was an absolute monarch in an age when not only Britain but the other Western European countries were liberalizing their laws and gradually becoming democracies. The Ottoman Empire was, of course, despotic as well, but it was weak, and Britain already was controlling it.
In summary then, both the conservative wish to maintain the status quo and a more liberal desire to defeat Russian authoritarianism animated British and French interests. At the same time, Russia was motivated by conservative religious factors and the desire to aggrandize its own power but also by liberal humanitarian concerns about the minorities in the Ottoman realm.