Anyone who works with members of the public will occasionally encounter difficult people. Different personality types are likely to be affected in different ways by this. And of course current mood and feelings of wellbeing will also have an effect.
Some job roles require people to deal with angry or upset people on a regular basis, and these jobs are likely to attract people who are comfortable dealing with these kinds of situations. Good training should provide enough skill, and if support is available as well, it is unlikely to affect wellbeing to any great extent.