You don't have to learn 'frequentist' or Bayesian statistics in any particular order. You should first learn whatever you need to understand the findings in your field, and then you should understand the mathematical (computation) and philosophical (interpretation) relationships between the techniques.

Should I study Bayesian statistics?

Bayesian Statistics helps to get rid of common mistakes and errors that we face in the traditional way of analysis and statistics. The results obtained with the help of Bayesian Statistics are easier to understand and better decision making is enabled with the help of this theorem.

How important is Bayesian statistics?

Bayesian statistics gives us a solid mathematical means of incorporating our prior beliefs, and evidence, to produce new posterior beliefs. Bayesian statistics provides us with mathematical tools to rationally update our subjective beliefs in light of new data or evidence.