Are filibuster opponents in favor of majority rule in the Senate?
No, not really. What they're in favor of is majority party rule.
That, as Emily Litella used to say, is very different. The House of Representatives, over the last fifty years, has increasingly featured majority party rule. That means the majority party gets to choose which bills come up for a vote, which amendments are allowed to be offered, what the voting rules for those amendments are...they get to manipulate things so that the majority party gets its way. But that doesn't mean that the majority is getting its way. Not everyone in the majority party agrees on every issue. But if the party controls the agenda, they can narrow that agenda to those things that do have widespread agreement from majority-party Members of the House, and prevent votes on amendments and bills that might get 218 votes from some combination that does not involved the majority of the majority party.
That was visible in the health care debate in the Senate. A majority favored a (weak) public option. A different majority favored drug reimportation. A majority opposed the CLASS act, so that would be gone. There may be a majority favoring stronger abortion language, somewhere between Nelson's deal and Stupak. If all those things pass -- and if it takes just fifty, Republicans might have been able to find a few more things that could pass -- then it's not clear that the resulting bill still has fifty votes. The public option goes in, and four to six Senators are gone. Drug reimportation might have lost a few more. If the abortion language moved even a little bit more in the direction of the pro-lifers, it's possible that a few pro-choice Senators might have refused to vote for it. There are some goodies in their for Bernie Sanders (community clinics, if I recall correctly); do they survive a vote? If not, does he stick?
The majority party gets quite a bit of influence on which of these things is called up for a vote, and which is not. They do that through the use of the committee system, and through floor rules. In the House, the mechanisms for majority party rule are strong; in the Senate, they are weaker, even without the filibuster. But still, they are useful for the majority party. Indeed, while the increased use of the filibuster has weakened majority rule in the Senate, at the same time changes in rules and norms (along with increased ideological consistency within the parties) have given party leaders a stronger hand to play. That's not majority rule; it's majority party rule.
I'm not saying, by the way, that this is necessarily a bad thing. It's just not simple majority rule.