It's just a perspective, but Bayesian inference makes the prior explicit, wheareas it is implicit with frequentist inference. You can't not have a prior.
A possible third approach is to create a hypothetical model and feed random data through it, to get an idea of the spread of the outcomes. Modeling doesn't stumble on conditional terms, and if you're unclear on an assumption, it won't run. The computer doesn't know whether it's a frequentist or a Bayesian, or something different from both.
I'm not a statistician. Whenever I need to do something with statistics, I always test my computation with random data.
In fact I wonder, if modeling had been possible since the birth of statistics, if we would even bother with things like elaborate formulas for statistical tests.
Subjective priors are one of the main advantages of Bayesian stats. Regularization used in ML corresponds to using subjective priors, for example. L2 regularization finds the MAP with a normal prior, favoring parsimonious solutions.