The reply to this misunderstanding:
First: It's ignorance to claim that Muhammad (PBUH) called for racism, as this is completely untrue, and it’s proved by the following:
1 – Allah, the Almighty, says in the Quran: {O mankind, indeed We have created you from male and female and made you peoples and tribes that you may know one another. Indeed, the most noble of you in the sight of Allah is the most righteous of you. Indeed, Allah is Knowing and Acquainted} (The Rooms:13).
2 – Muhammad (PBUH) said: "There's no priority for an Arab over a foreigner, nor a foreigner over an Arab, nor a white over a black, nor a black over a white, except by piety. People were created from Adam, and Adam was created from mud".
3 – Al Termithi's Sunan, no. 3193. Ibn Omar (may Allah be pleased with him) narrated that the prophet (PBUH) gave a sermon on the day of entering Makkah victrious, he (PBUH) said: "O people, Allah has saved you from the racism of the era before Islam. People are two types: a pious, sincere, lovable to Allah, and a bawdy, disobedient, unlovable to Allah. People were created from Adam, and Allah created Adam out of mud, Allah says: {O mankind, indeed We have created you from male and female and made you peoples and tribes that you may know one another. Indeed, the most noble of you in the sight of Allah is the most righteous of you. Indeed, Allah is Knowing and Acquainted}".
Second: Their claim that Muhammad (PBUH) called for racism even in greeting non-Muslims, is false, and this is proved by the following:
1 – The Correct Series, no. 569. The prophet (PBUH) said: "O people, spread peace, feed the poor, care for your relatives, and pray at night while people are sleeping, you shall enter paradise in peace".
2 – Ibn Majah's Sunan, no, 3692. Abu Huraira narrated that the prophet (PBUH) said: "You shall not enter paradise as long as you do not affirm belief (in all those things which are the articles of faith) and you will not believe as long as you do not love one another. Shall I direct you to a thing which, if you do, will foster love amongst you?: spread peace among you (the practice of greeting one another by saying assalamo alaikum (peace be upon you)”.
3 – The Correct Bukhari, no. 11. Abdullah Ibn Amr (may Allah be pleased with him) narrated that a man asked the prophet (PBUH) saying: "What are the best deeds in Islam?" The Prophet (PBUH) replied, 'To feed the poor and greet (say: peace be upon you) those whom you know and those whom you do not know".
Notice: "greet those whom you know and those whom you don't know".
4 – He (PBUH) ordered to be generous with the guest, even if he/ she was a non-Muslim. This is mentioned in The Correct Bukhari, no. 5559, Abu Huraira narrated that the messenger of Allah (PBUH) said: "Anybody who believes in Allah and the Last Day should not harm his neighbor, and anybody who believes in Allah and the Last Day should entertain his guest generously and anybody who believes in Allah and the Last Day should say what is good or keep quiet. (i.e. abstain from all kinds of evil and dirty talk)".
5 – He (PBUH) ordered his companions to treat all people with good manners. This is mentioned in Al Termithi's Sunan, no. 1910, Abu Zarr said: the messenger of Allah (PBUH) said to me:"Fear Allah wherever you are, make a good deed after committing a sin, so that it shall be eliminated, and treat people with good manners".
6 – Allah, the Almighty, ordered His messenger (PBUH) in the Quran saying: {and speak kindly to mankind} (The Cow:83).
Mankind means; all people, the believers and the disbelievers.
Thus, the previous evidences prove that this misunderstanding is completely false and untrue.
Second: The objectors misunderstood the prophet's (PBUH) speech, which says: "Do not greet the Jews and the Christians before they greet you and when you meet any one of them on the roads force him to go to the narrowest part of it".
The speech doesn't call for racism as they understood, it rather has a different meaning, which can be clarified through the following question: if someone insults your father, what shall you do?