Look at the most modern open source R and Python packages for statistical inference… probably 90 percent are developed and maintained by social science research labs
Bayesian statistics is great, you can get any posterior you want by choosing good priors.
"This study provides 5dB of evidence that the pigs do not reactionless flight capabilities, and 300dB of evidence that I don't know how physics works. However, according to my priors, the flying pigs hypothesis still comes out ahead." said no study ever.
It's best to model journals as magazines that publish anything that vaguely resembles science (has equations, charts, citations, claims of data). It doesn't have to actually be science. If you want to get a paper published it's totally normal to write 10,000 lines of C or FORTRAN, claim it models some natural process, publish a paper with the graphs it outputs and call it a day. The code isn't available. The input data isn't available. The assumptions aren't documented properly or at all. And the outputs are unvalidated, therefore not even laying the foundations of being evidence of anything. Doesn't matter, it'll get published, in some fields this is the vast majority of what gets published (e.g. epidemiology).
Personally, I always use a uniform prior unless I am able to cite or present the data that led to something else.
The best experimenters I know in terms of monitoring and controlling external variables are chemists, but sometimes they just use the wrong statistical test.
Biologists seem to generally be bad at both, and physicists seem to generally be good at both. I honestly think this is about the culture of the fields rather than knowledge - they all start as good scientists and just unlearn what they don't "need."
IMO, mathematical and computational “literacy” is particularly low in the medical and life sciences compared to the social sciences, physics and chemistry are not quite as bad.