Whichever group seeks to push its values on others via force or compulsion will find a reason to dismiss or vilify freedom of expression and speech. Then all other groups will band together to oppose that first group of would-be tyrants. Claiming that there's something psychologically distinct about one political party or another at an individual level (which goes beyond a mere snapshot or moment in time) is to see them as ideologically driven monoliths, when they are in fact hodgepodge collectives of various interest groups.

Conservatives will support freedom of speech so long as it is a winning strategy politically and they make a cultural space for those seeking to circumvent top down censorship. Blasting this approach as disingenuous is clear cut coping. If liberals want to champion free speech, then let them do so. People are flocking to conservative parties because the ostensibly liberal ones have given them no other option. Don't blame the conservatives, even if you think this is opportunistic. Instead get your own house in order and be glad that oppositional politics provides enough incentives to ensure at least one party will champion the cause for freedom of expression, regardless of the ideological justifications they use to get there.