Bayesian analysis is certainly nothing new, but particularly in the social sciences I feel there is a bit of institutional inertia. Slowly but surely people are moving away from thumbs-up/thumbs-down hypothesis testing, magic “p < 0.05” thresholds, and point-and-click recipes.
I think a vital ingredient in obtaining greater acceptance of Bayesian methods is the availability of introductory stats textbooks that start out Bayesian, rather than leaving it to an appendix after thoroughly confusing students with frequentism. Software tools and hands-on simulation should be embedded in the curriculum from the first week, and forget about asking students to calculate sums-of-squares by hand!
Richard McElreath has recently completed a textbook aimed for social science grad students (so don’t worry, it is not dauntingly technical!) which works up from linear regression to generalized linear multilevel models (aka mixed-effect, including repeated-measures). And does it all from a Bayesian perspective, including abundant examples in R to illustrate how to build your own models. I recommend it!
Statistical Rethinking, by Richard McElreath