Identify a card game where players are asked questions about life situations
I'm assuming this game an English-language party game printed in the United States, because that's what I know best, but variants of the "who would X" mechanic have been published for decades in many countries.  That said, searching BoardGameGeek for party games with social mechanics (particularly voting on other players) and limiting the list of games to those published in the USA from 1970 to 1999 gives four likely candidates:

True Colors (1990):  Cards show a question, and you vote on who best fits it - and try to bet how many players will choose you.  Questions are things like "WHO would still clip coupons after winning five million dollars in the lottery?" and "Flirting is an art, WHO is the undeniable expert?"  Has been published under other names and in several art styles, the link shows the box and components from the 1990 Pressman edition.  Closest match in mechanics and publication date.

The Ungame (1973):  This roll-and-move "board game" is more about explaining yourself to other players or discussing other players.  Questions include "Talk about a happy marriage." and "Share a childhood experience with death."  Not the closest match for mechanics or publication date, but it sold like hotcakes so worth mentioning.

Family: The Game (1990):  A board game about dealing dirty laundry about family members, questions include things like "When it comes to smelly feet, our family's champion would have to be _____!"  Not a very popular game and it doesn't use cards, but it's otherwise a very close match for mechanics.

Who Said That? (1998):  A card-based board game, everyone writes an answer to a question like "You're in a bar and find a wallet full of money, what do you do?" and you try to guess who gave what answer.  Close match in mechanics but published a few years after the "early 90s."

Speaking personally, this is also how most of my games of Nomic and 1000 Blank White Cards end up, but neither game has set cards.