It seemed that every time that I used “me and x” I was corrected to say “x and I”. They never gave a reason why it should be “x and I” so it seemed like it should always be that way. I imagine that there were cases where I wasn’t corrected because “me and x” was the correct way to say it but you don’t remember when they don’t correct you.
For convoluted linguistic reasons, "x and me," is correct and the default expression in English for this type of subject. If I recall, "x and I" is how it would be said in Latin, and I believe the desire to sound more educated // "proper" (like Latin) was the original reason that this phrase was pushed onto children in schools, by well-intentioned but ignorant school masters.
If "me and my twin" is a short form of the sentence "This is me and my twin." then it is actually more correct to say "This is I and my twin."
So I think this is just language drifting. In English, we use the objective under posts like this. That is to say that "Me" is what you'd normally say to post this. But that's because language has shifted so that "This is I." sounds wrong. (To be clear, it is proper.)
In German, you would use the nominative here. That is "ich" translating to "I". I believe English is the outlier here when we consider what grammatical case most languages would use here.
To be clear "Me and my twin in the 80s." is not wrong. But if you needed it to be a proper and complete sentence "This is my twin and I in the 80s." is correct.