Messenger is sent to people who reject and deny him. According to who was that opinion based on, and what evidence do we have for it?

It was Sheikhul Islam ibn Taymiyah, who concluded this opinion. However, there are numerous verses in the Qur'an to allude in favor of this opinion.[1]

كَذَٲلِكَ مَآ أَتَى ٱلَّذِينَ مِن قَبۡلِهِم مِّن رَّسُولٍ إِلَّا قَالُواْ سَاحِرٌ أَوۡ مَجۡنُونٌ

Likewise, no Messenger came to those before them, but they said: "A sorcerer or a madman!" [2]

This shows that every messenger was rejected by his people by coining vile names for him.

مَّا يُقَالُ لَكَ إِلَّا مَا قَدۡ قِيلَ لِلرُّسُلِ مِن قَبۡلِكَ‌ۚ إِنَّ رَبَّكَ لَذُو مَغۡفِرَةٍ۬ وَذُو عِقَابٍ أَلِيمٍ۬

Nothing is said to you (O Muhammad ﷺ) except what was said to the Messengers before you. Verily, your Lord is the Possessor of forgiveness, and (also) the Possessor of painful punishment. [3]

References:

[1] http://islamqa.info/en/11725

[2] Surah Dhariyat Verse 52

[3] Surah fussilat verse 43