Salam (Peace) Dear Bryan,
Thank you for contacting About Islam with your question.
The simple, straightforward answer to your question is: no, the Prophet Muhammad (peace be upon him-PBUH) never made such remarks or any other remarks even close to this.
In fact, the opposite is true, since the Prophet (PBUH) was always in support of human rights and since the very first day of his mission as a prophet, he launched a war against discrimination of all types and on all levels.
When the Prophet (PBUH) was instructed to go out and deliver the message, he was told that one of the main characteristics of this message of Islam is that it establishes equality between all people, regardless of their colors, backgrounds, languages, or socio-economic status in the society.
That was actually one of the challenges that faced the Prophet since the early days of Islam. The polytheists of Arabia refused to be associated with their slaves, who, at that time, were very much downgraded and ill-treated in society.
The very concept that they and their slaves stand on equal footing in terms of treatment and religious liability was very annoying to these arrogant Arab idolaters. That was probably one of the main reasons that led them to reject the emerging call of Islam and see it as a threat to their false sense of “dignity” and discriminatory policies.
They saw such a call to equality between all people as a devastation of their business and society that depended to a great deal on trading in slaves.
When Prophet Muhammad came, he advised them that no human being is better than another except by the merit of righteousness and pious God-consciousness. He told them also that all people are equals in the sight of Allah as the teeth of one comb and therefore, each one in this universe deserves respect regardless of his or her color or background.
He announced a human brotherhood where people stand on equal footing as brothers and sisters in front of Almighty Allah and He alone can judge them. He also taught them that Allah does not look at the appearance or the form, but He sees hearts and looks at deeds.
All these revolutionary teachings alarmed the leaders of the Quraish tribe of Makkah and gave them an excuse to amass their allies against the Prophet Muhammad (PBUH).
Yet, he did not give up. Rather, he went on to teach people that their Lord is one, and that all of them are the sons of Adam who was created from dust.
This call brought him the love of the weak and the oppressed as well as the slaves who embraced Islam in big numbers.
The Prophet could have saved himself all this hassle and could have told the leaders of Makkah what they wanted to hear, but he was a man with a mission and his message was to be delivered the way Allah wants, not the way people wish to hear it.
In the Muslim community, there was no shame at all for some great Companions who were, just some time before this, in leading positions in Makkah to sit with a black slave like Bilal ibn Rabah and learn from him.
Bilal was even called “our master” by the Prophet’s companions, referring to his great status which he gained by merit of his knowledge, dedication, and sincerity.
The Prophet was able to change the ideas of Arabs who, after embracing Islam, were happy to unite with their ex-slaves, and then Muslim brothers, in perfect unprecedented brotherhood.
Any incident, gesture, or hint that could annoy this brotherhood was taken seriously by the Prophet. When The Prophet’s Companion Abu Dhar Al-Ghifari unintentionally annoyed his brother Bilal by calling him the “son of a black woman”, the Prophet took it very seriously and was alarmed at that instance that such a phrase was a threat to the well-established brotherhood.
Therefore, he did not let it pass. Rather, he turned to Abu Dhar and said: “Are you calling him by the color of his mother? You are a man who still has traces of pre-Islamic ignorance.”
That instance was so alarming to Abu Dhar who, realizing his mistake, rushed to seek forgiveness from his brother Bilal and placed his head on the ground asking Bilal to step by his shoes on his face as a way of making him feel, to some extent, the offence he has directed to him.
Yet Bilal, who realized that Abu Dhar had understood the lesson, and that the insult was completely unintentional, took his hand and hugged him in a brotherly gesture.
In that society there was no place for discrimination as it was uprooted from the hearts before the minds. All considerations about color and class superiority were taken away from the worldview of Muslims.
Such a great achievement and change happened in Arabia almost 1300 years before the civil rights movement emerged in the US.
Prophet Muhammad (PBUH) did not have to establish laws to get something like this done, because he knew it does not come from the law, but rather, from the heart of faith.
I hope this answers your question.