A sufficiently dedicated group can do that, but if you don’t see why it’s difficult to bring the listed cards out I can’t help you. There’s no reason to have most of them in this deck as a creative group that can have fun with them isn’t really having a better time for their inclusion over more creative cards. There’s absolutely no reason for cards like “slutty” and the host of cards about play-acting mental illness in a short and snappy improv game are extremely unsafe inclusions.
You’re not reviewing the cards, you’re reviewing your friends. You’re right, it is up to the players. And players who don’t want to do something unpleasant will frequently find themselves spending time and energy feeling awkward and trying to get rid of cards like this rather than having fun.
P.S. This speaks to a broader issue with the design of games like Funemployed and CAH in particular; these are improv games where you’re trying to please a crowd and work within the social contract of that space, but where no one at the table has any input into what does and doesn’t come up. Everyone who buys these games is effectively trying to sit at the table with the ghost of the designers and their friends; that’s not going to work or be safe for a lot of people who have never met the designers and their friends. Some games in this genre put less stress on this sort of content and more stress on the scaffold you build around it; CaH and Funemployed are card-content heavy and that’s where a lot more problems come up.