It depends on time and place. In Israel and Western Europe I will take the "democracy" side of the argument every time (which, in Israel, is paradoxically the side that isn't talking about democracy all the time because the definition is so distorted), but in places such as Turkey and Egypt I'll gladly go with the "anti-democratic" alternative if necessary. Needless to say I supported the failed coup.
In Israel, the right tends to prioritize Knesset decisions over more liberal-democratic inclined decisions or advise, such as by the Supreme Court or NGOs. By contrast, the left seeks to diminish the importance of Knesset decisions by involving many other actors (which is what they call democracy, and while I, as a political scientist, obviously see the theoretical case for doing so, I consider it a bit of a distortion because it doesn't have much to do with the "demos"). This is similar to what we see in Western Europe: "populists" and eurosceptics want the decision-making process to mainly take place in parliament and support referendums, thereby adhering to a very electoral definition of democracy, whereas most established, mainstream political forces think it is good to involve many other actors and make sure not much power is in the hands of parliament, which they see as important in guarding liberal democracy. I would say the contrast is not the same and the actors are not the same, but there are definitely important similarities.
In both contexts I support the ones who adhere to a more electoral conceptualization of democracy, because I believe it is important that large majorities agree with policies and there should be a very direct link between the majority's vote and the policies that are eventually implemented, more so than is now the case.
Sorry as a political scientists you should be familiar with Kelsen hierarchy of norms. If there are constitutional norms (I'll go with on the case study - the Knesset legislated constitutional basic laws) the court must examine legality of primary and secondary legislation accordingly. That is the electoral desire (otherwise no constitutional norm would have been created) and that is the common law of the land.
So basically that was the democratic wish of the people de jure. It also not so much that the right respects Knesset legislation more as parts of it think there should be constitutional voids where it should not interfere with the political act (especially in relation to the Palestinians). So it's more of Schmitt vs Kelsen debate all over again, but it's not liberalism vs democracy per se.
If anything you could say right wing prefer a more European conception of separation of powers with more judicial deference to the legislator while the left (not just here) prefers a strong judicial branch common law like to be a counter balance to the threat of majority power.
As to political philosophy I see no intrinsic value in collective decision making in itself, without the human rights I can't see a strong justification for it unless you accept communitarian conception of morality (see niko kolodny 2014) which I believe are shaky at best
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