Are possibly outdated and damaging studies being taught in universities, and should I be worried?
Some parts of the field of Psychology move very quickly. The pace of the field makes keeping course up to date difficult. For example, in 2013, there was a major update to the DSM. Some classes were ignoring DSM-IV and teaching based on what eventually made it into DSM-5, others kept teaching based on DSM-IV. Some of these classes are still being taught on DSM-IV, despite the new guidelines since it takes time to get new text books and revamp lectures. The same thing happens with courses that look at pharmaceutical treatments and drug addiction. The fields move too quickly to keep up, and many teach based on a snapshot of the world.

As for cutting edge research, Psychology, like many fields has lots of great research and lots of questionable research. Not all Psychology programs get so far as to expose students to cutting edge research. Those that do, tend to try and teach students to read critically.

In summary, the point of a degree is to become a critical thinker. The fact that there are alternative theories is not something to worry about, but rather something to embrace.