What people also tend to misunderstand that Popper and also logical positivists provided a normative picture of what science ought to be be, rather than what it is. This naive normative picture of the scientific method was (perhaps even now it is with many scientists) in vogue during the 1950-60s, for example look at Medawar's books who was heavily influenced by ideas of Popper. The very fact that scientists do not give up on their pet theories despite of contrary evidence is a good evidence against such simple views, which have an image of a scientist as someone without any human emotions and personal beliefs.
Also associated are several ideas of science being value neutral and observations being theory agnostic which were foundational to these view points have been seriously challenged.
The idea that we ought to believe what's true is itself a normative picture of how humans should think rather than a descriptive picture of how humans do think.
There's no scientific way around underdetermination, but there certainly are a number of philosophical ways around it.
Starting with: I'll believe whatever the heck I want to believe.
Also associated are several ideas of science being value neutral and observations being theory agnostic which were foundational to these view points have been seriously challenged.