I think my mind has been affected by the nanny state - jokes I would usually find funny and harmless are making me think whether I can laugh any more at a minority group. made me feel uncomfortable - like I cant chose what I think any more.
What do you feel when you read it.
https://www.theanswerbank.co.uk/Phrases-and-Sayings/Jokes/Question1602645.html
My younger brother has a bit of a stammer, it has got better in more recent years, I know he would have found it funny. As it has been mentioned the joke was not aimed at him more with him.