An “ID card” with no photo?
Not even a unique identifier (card number)?
No official state seal — the kind that would be hard to duplicate?
Just a basic one-color (red) ink card on white paper stock that any Kinko’s could do?
Even in 1984 this is hard to believe.
In the 1970s and 1980s in Canada social insurance insurance numbers cards were printed on plastic cards that just showed your name and number, no photo ID or address.
https://www.680news.com/wp-content/blogs.dir/sites/2/2017/07/sin_card.jpg
I'm not sure what they do with it now but back at the time of the movie, you could have an ID card without much info.
As for the Ontario health cards, I can imagine it was the same - some health cards now have your name and address but back then, maybe not.