The GMB presenter raged after Mr Oluwole criticised his social media friendship with US right-wing commentator Ben Shapiro.
Mr Oluwole tweeted: “Bit of advice… He’s not good company to keep. Not a good look, but you do you…”
Mr Morgan fired back: “Thanks for the tip, Femi, but I really like Ben Shapiro – he’s one of the smartest and fairest thinkers in America.
“It’s being friendly with you that’s more damaging to my brand.”
Another critic of the high-profile Remainer tweeted: “The problem with Femi is that he thinks everyone should think like him, but if everyone did, nobody would know who he was because he’s made a career out of slagging off anyone who thinks differently.”
Another said: “The arrogance from Femi is unreal.”
And another said: “Who even is this Femi person? And why do they think they matter? Were they once on Big Brother?”
READ MORE: ‘Woke PC gone mad!’ Fury over gender-neutral Mr Potato Head
The spat began when Mr Morgan and Mr Shapiro both responded to news that Mr Potato a classic American toy, is going to become gender-neutral according to Hasbro, the company which makes it.
The toy will become known as “Potato Head”, losing the “Mr” from its name.
Similarly the boxes it’s sold in will be called “Potato Head” rather than “Mr Potato Head”.
Mr Potato Head, first sold in 1952, is a potato-shaped toy that mimics the human face.
Mr Morgan tweeted: “Imagine thinking in the middle of a global pandemic: ‘What’s really important is dropping the ‘Mr’ from Mr Potato Head & making him gender-neutral in case we upset a few wokies.’”
Mr Shapiro joked: “Now any child, of any gender, can look at a Potato Head and dream of growing up to be a plastic spheroid with interchangeable parts.”
The conservative commentator courted controversy after the US elections when he called on Joe Biden’s wife Jill to stop referring to herself as “Dr” and said only those with degrees in medicine or hard science should use the title.
The First Lady is not a medical doctor but rather holds a doctorate or PhD in education from the University of Delaware.
He continued: “Having watched my wife do the latter, it simply isn’t comparable.
“You’re at a dinner and somebody introduces himself as ‘Dr Smith’ – you’d be rather upset to learn that he had a doctorate in musicology if you were to suffer a stroke at the table.”