Caveat: I'm not a professional statistician. My impression as a student, however, is that among statisticians, Bayesian statistics is viewed as a part of the m

Caveat: I'm not a professional statistician. My impression as a student, however, is that among statisticians, Bayesian statistics is viewed as a part of the mainstream way of doing statistics. So it has perfectly okay reputation in that sense. But when it comes to applications, the extent that Bayesian methods are used varies between fields quite much. In machine learning and computational statistics community, it seems to be very popular. On the other hand, ome other fields (esp. the published papers) appear still to be mostly about hypothesis testing and p-values. (For example, last time I checked, the "Introduction to Statistics for Social Scientists" first undergrad level course in our uni was mostly about the traditional frequentist stuff.)