Please keep in mind that stuff like this is highly culture- and context-dependent. Try to word it in such a way that doesn't sound like it's universal. Maybe add some sections sorting this by country/culture.
"We should get coffee sometime" or similar phrases (we should do ____ sometime) are often used by neurotypicals to politely convey interest in socializing with other people. However, these are mostly used to be polite and are not actual plan requests, which creates a conflict between the neurotypical person relaying this message and the autistic person receiving it. Autistic people's tendency to interpret things literally means that they will expect the plan to be followed up, while neurotypical people rarely have the intention to lead this plan to fruition. That creates a sense of rejection in the autistic person due to their different expectations.
I have found that people say this when they would actually like to maybe hang out with you, or just get to know you better! "Getting coffee" is almost like a "codeword" of sorts for hanging out in general. I would generally take this as a compliment, as I have found that people are USUALLY genuinely trying to convey interest in you when they say this. Unfortunately, "We SHOULD get coffee sometime" is not an actual, solid plan. It is a suggestion. Therefore, the next step in this situation is for you or the other party to take the initiative to formulate an actual, solid plan. This does not always happen, but that does not mean that the person who suggested this never actually WANTED to hang out with you! Sometimes even autistic people may say "we should get coffee sometime" as a less anxiety-inducing way to try to suggest that they WANT to make plans, but by saying this, that is not a guarantee that they WILL make an official plan. Once someone does take this first step (which can require bravery!), either party may or may not take the next step, which would be making a solid plan. (Whoever wrote the above: please don't be offended that I had this alternate perspective! I think it can be important to demonstrate on this wiki that different people can have different perspectives depending on their unique knowledge and experiences. I respect the other perspective shown above!)
Also: this can vary by country. In some countries, statements like this might always mean "Let's have coffee/whatever!"