Does the father’s country of origin or the mother’s colour prevent their son from becoming Muslim?

What you mention does not stop you from becoming a Muslim at all. Islam is
the religion for all of mankind, no matter what their colour, land, tribe or language. The
Prophet Muhammad
(peace and blessings of Allaah be upon him) is the Messenger to all
of mankind, of all origins and countries. Allaah says (interpretation of the meaning):

“Say (O Muhammad): ‘O mankind! Verily, I am sent to you all
as the Messenger of Allaah – to Whom belongs the dominion of the heavens and the
earth. None has the right to be worshipped but He; it is He Who gives life and causes
death. So believe in Allaah and His Messenger, the Prophet who can neither read nor write,
who believes in Allaah and His Words, and follow him so that you may be guided.”
[al-A’raaf 7:158].

There is no superiority of anyone over anyone else in Islam, except in
terms of taqwa (piety, consciousness of Allaah). Allaah says (interpretation of the
meaning):

“O mankind! We have created you from a male and a female, and made
you into nations and tribes, that you may know one another. Verily, the most honourable of
you with Allaah is that (believer) who has al-taqwa (i.e., is one of the muttaqoon –
the pious). Verily, Allaah is All-Knowing, All-Aware.” [al-Hujuraat 49:13]

In His wisdom, Allaah has made mankind into different peoples and tribes
so that they may know one another, not so that they may despise one another. He tells us
that the differences in colour and languages are a sign of His greatness and power in
creation. He says (interpretation of the meaning):

“And among His Signs is the creation of the heavens and the earth
and the difference of your languages and colours. Verily, in that are indeed signs for men
of sound knowledge.” [al-Room 30:22]

The Prophet of Islam, Muhammad
(peace and blessings of Allaah be upon
him) affirmed the prohibition of racial discrimination and of despising coloured people,
when he said in his famous speech: “O people, your Lord is One and your father [i.e.,
Adam] is one. There is no superiority of the Arab over the non-Arab, or of the non-Arab
over the Arab, or of the red over the black, or of the black over the red – except
with regard to taqwa.”

(Reported by Imaam Ahmad, 22391)

When a man insulted his brother (in Islam) for having a
black mother, the Prophet
(peace and blessings of Allaah be upon him) said to him,
“You are a man who still has jaahiliyyah (ignorance) in him.” Abu Dharr (may
Allaah be pleased with him) said: “There was an argument between me and one of my
brothers whose mother was non-Arab. I insulted him about his mother, and he complained
about me to the Prophet
(peace and blessings of Allaah be upon him). I met the
Prophet
(peace and blessings of Allaah be upon him) and he said, “O Abu Dharr,
you are a man who still has jaahiliyyah (ignorance) in him.”

(Reported by
al-Bukhaari and Muslim; this version narrated by Muslim, 3139).

Hasten to Islam, and you will prosper. You will find in
Islam that which will delight you in this world and the next. Peace be upon those who
follow true guidance.