Generally, yes, especially regarding a new advancement, form, or format. When critics and audiences alike are aligned about something new, it's often taking into account the expertise of the critic in addition to the sympathies of the layperson's appreciation of the form. Both sides of the coin are covered. One on hand, you get a careful consideration of the form and all that has come before it, on the other hand, in terms of music, you get whether or not the noise is palatable to the listener. Raw theory won't suffice, it has to sound good, too, for the audience to appreciate it. Nor will simple and redundant songs and lack of innovation be rewarded; that's the critics job.
Taylor Swift has made hand over fist in cash out of careerist-minded vulnerability and often overdone hurt at the slightest of slights. It's no wonder she sang that song.
And yes, musicians put up with critics but I'd bet no critique moves them so much as a review that is sound critically
and praises their particular work for being forward-thinking. No doubt in my mind. Of course, there are some people that want nothing to do with the whole game, but often that impulse comes just as much from the artist believing it's their proper place to assume the prominent critical role through the musical composition itself. Indeed, often the artist thinks it is his or her role to be the critic of him or herself because other people either are too simple, too narrow, or just don't get what they're trying to do. I think of Van Morrison when I think of that attitude.
So yeah, you get a lot of people that don't like critics, but they run the gamut from those who are not praised by critics for a host of valid reasons to those who don't like critics because they think critics are not their proper intellectual peers. There's a lot of that. Doesn't mean it's right. Simply because the artist (or artists) eschews criticism does not impugn the validity of the opinion of a learned critic.