There is no compulsion to accept Islam

The scholars explained that these two verses, and other similar verses, have to do with those from whom the jizyah may be taken, such as Jews, Christians and Magians (Zoroastrians). They are not to be forced, rather they are to be given the choice between becoming Muslim or paying the jizyah. 

Other scholars said that this applied in the beginning, but was subsequently abrogated by Allah’s command to fight and wage jihad. So whoever refuses to enter Islam should be fought when the Muslims are able to fight, until they either enter Islam or pay the jizyah if they are among the people who may pay jizyah. The kuffaar should be compelled to enter Islam if they are not people from whom the jizyah may be taken, because that will lead to their happiness and salvation in this world and in the Hereafter. Obliging a person to adhere to the truth in which is guidance and happiness is better for him than falsehood. Just as a person may be forced to do the duty that he owes to other people even if that is by means of imprisonment or beating, so forcing the kaafirs to believe in Allah alone and enter into the religion of Islam is more important and more essential, because this will lead to their happiness in this world and in the Hereafter. This applies unless they are People of the Book, i.e., Jews and Christians, or Magians, because Islam says that these three groups may be given the choice: they may enter Islam or they may pay the jizyah and feel themselves subdued. 

Some of the scholars are of the view that others may also be given the choice between Islam and jizyah, but the most correct view is that no others should be given this choice, rather these three groups are the only ones who may be given the choice, because the Prophet (peace and blessings of Allah be upon him) fought the kuffaar in the Arabian Peninsula and he only accepted their becoming Muslim. And Allah says (interpretation of the meaning): 

“But if they repent [by rejecting Shirk (polytheism) and accept Islamic Monotheism] and perform As-Salaah (Iqaamat-as-Salaah), and give Zakaah, then leave their way free. Verily, Allah is Oft-Forgiving, Most Merciful”

[al-Tawbah 9:5]

He did not say, “if they pay the jizyah”. The Jews, Christians and Magians are to be asked to enter Islam; if they refuse then they should be asked to pay the jizyah. If they refuse to pay the jizyah then the Muslims must fight them if they are able to do so. Allah says (interpretation of the meaning): 

“Fight against those who (1) believe not in Allah, (2) nor in the Last Day, (3) nor forbid that which has been forbidden by Allah and His Messenger  (Muhammad), (4) and those who acknowledge not the religion of truth (i.e. Islam) among the people of the Scripture (Jews and Christians), until they pay the Jizyah with willing submission, and feel themselves subdued”

[al-Tawbah 9:29]

And it was proven that the Prophet (peace and blessings of Allah be upon him) accepted the jizyah from the Magians, but it was not proven that the Prophet (peace and blessings of Allah be upon him) or his companions (may Allah be pleased with them) accepted the jizyah from anyone except the three groups mentioned above. 

The basic principle concerning that is the words of Allah (interpretation of the meaning): 

“And fight them until there is no more Fitnah (disbelief and polytheism, i.e. worshipping others besides Allah), and the religion (worship) will all be for Allah Alone [in the whole of the world]”

[al-Anfaal 8:39] 

“Then when the Sacred Months (the 1st, 7th, 11th, and 12th months of the Islamic calendar) have passed, then kill the Mushrikoon (see V.2:105) wherever you find them, and capture them and besiege them, and lie in wait for them in each and every ambush. But if they repent [by rejecting Shirk (polytheism) and accept Islamic Monotheism] and perform As-Salaah (Iqaamat-as-Salaah), and give Zakaah, then leave their way free. Verily, Allah is Oft-Forgiving, Most Merciful”

[al-Tawbah 9:5]

This verse is known as Ayat al-Sayf (the verse of the sword). 

These and similar verses abrogate the verses which say that there is no compulsion to become Muslim. 

And Allah is the Source of strength.