Indeed there are people who hold this view and even quote the Qur'an to support their actions but this is a gross misunderstanding of the Qur'an, of the historical contexts in which the verses were revealed and due to their own inherent tendencies towards extremism. You may also find such statements from non Muslims who want to tarnish the image of Islam.
One of the verses which may be quoted to support this errant view is Qur'an 9:5
And when the sacred months have passed, then kill the polytheists
wherever you find them and capture them and besiege them and sit in
wait for them at every place of ambush.
However, the verse is clearly referring to the Meccan polytheists and not just any disbeliever. Secondly, the Qur'an didn't say just kill any polytheist, but only those whom had broken their treaty with the Muslims (see the previous verse9:4).
In another verse, the Qur'an explicitly makes it clear that the order to fight the disbelievers is only with regards to those who fight the Muslims or help others in fighting the Muslims (Qur'an 60:8):
Allah does not forbid you from those who do not fight you because of
religion and do not expel you from your homes - from being righteous
toward them and acting justly toward them. Indeed, Allah loves those
who act justly.
There are many verses of the Qur'an, too numerous to list all, that establish that man has been given the free will to believe or to disbelieve. Don't forget people are believers or disbelievers only according to Allah's will: if Allah had willed, everyone would have been a believer, and so killing people simply because of their disbelief is contrary to the will of Allah (Qur'an 10:99).
And had your Lord willed, those on earth would have believed - all of
them entirely. Then, [O Muhammad], would you compel the people in
order that they become believers?
You may wonder, how would the Prophet debate with disbelievers on religious issues, settle disputes between them, eat their food, accept their gifts, sign treaties with them, and even in one instance stand up in respect of a Jew that had died, if he also ordered to kill them? Does that make sense? How would the Qur'an say we're allowed to marry women from the People of the Book if we're supposed to kill them? Would you kill your own wife or inlaws?
In a summary, this is a minority extremist view, or one held by ignorant critics of Islam, and we have a duty to point out the errors of anyone who might be inclined towards this.