[Magdalen] The word “me”

[Allan Carr]

I read messages in a group called Nextdoor. Most of my neighbors here in Southern California never use the word me, as in “A dog attacked my dog and I” (an actual sentence I just read).
This is so common, even in newspapers, that I’m wondering if what we used to call the first person objective case “me“ has become obsolete in standard American English.
If not, the proper usage is no longer drilled in school as it was years ago. 
Is the word “me” now obsolete?

Allan Carr