The short answer is ‘No’.
In Islam, salvation is purely dependent on one’s personal relationship with God irrespective of their religion.
Therefore, the decision of who goes to heaven and who goes to hell is left entirely to God; He alone knows people’s hearts and is aware of their deeds. What Islam claims is that it is the perfect religion for mankind and a religion for all time and all people.
“This day have I perfected your religion for you and completed My favour upon you and have chosen for you Islam as religion.” (Ch.5:V.3)
Islam therefore certainly does claim to offer the best guidance – which if followed, leads to paradise – but simply being a Muslim is not enough to enter paradise.
It is the righteous who are rewarded by God, who may well be Muslims, Christians, or Jews, or people of other faiths.
The Qur’an states that people who do good deeds will be rewarded for them:
“For those who do good deeds, there shall be the best reward and yet more blessings.” (Ch.10: V.27)
So, it leaves it open to God as to who will be judged worthy of entering paradise. Islam also tells us the qualities of those people who will enter paradise:
“Surely, those who believe and do good deeds, and observe Prayer and pay the Zakat, shall have their reward from their Lord, and no fear shall come on them, nor shall they grieve.” (Ch.2:V.278)
In the above example, those who believe in God, do good deeds, act righteously, observe prayer and give to charity are promised to be rewarded by God – and this may include the ultimate reward of being admitted to Paradise in the Hereafter.
“Surely the believers and the Jews and the Christians and the Sabians – whichever party from among these truly believes in Allah and the last day and does good deeds – shall have their reward with their Lord and no fear shall come upon them, nor shall they grieve.” (Ch.2:V.63)
If a person rejects Islam after knowing Islam and fully understanding its truth, they will be judged accordingly by God. Otherwise, he will be judged according to his own religion or his understanding of right and wrong.