They had many episodes that referenced to events in real life at that time.
Several episodes were about the Vietnam War (link)
This website is about the social statements Star Trek made in the 60’s.
You could also check Memory Alpha. The Background Information on the episode pages often say about what event in real life it was based.
Many, many papers and books have been written about Star Trek. I suggest you dig around in Google a bit and you will surely find what you need.
If you have any other questions, feel free to ask, but please don’t do it anonymously. I’d prefer to answer questions like this privately.