Sure, tyranny of the minority is one of the reasons to be cautious about listening to loud voices and saying "Well, it's democracy, what can you do?" - you want to make sure the mechanisms you've chosen for implementing democracy actually do represent the will of all the people.

However, the loudest voices against lockdowns, masks, and other measures in the US seem to be associated with the minority-but-ruling party in this country.

It is true that the US is a federation of states, and it's a majority party in several states. In those ones, sure, I agree that a respect for the principles of democracy means that the people could choose differently. But if you've come to the point of arguing, "The real problem here is that anti-democratic policy X is being enacted with the support of the people," it's worth taking a moment to ask if policy X actually is democratic, and if saying "We should avoid policy X even if the people support it" is the actual tyranny of the minority.