I read that his reasons were, "If those books are in agreement with the Quran, we have no need of them; and if these are opposed to the Quran, destroy them." How were his actions viewed by others?
There are no known contemporary opinions— perhaps because there was no such event to form an opinion about.
Entire books have been written on the loss of the library, but I would first note that most historians reject this story as scurrilous. In fact, the orientalist Bernard Lewis, not ordinarily considered a propagandist for Islam, wrote an essay entitled "The Arab Destruction of the Library of Alexandria: Anatomy of a Myth" which appears in What Happened to the Ancient Library of Alexandria? by Mostafa el-Abbadi and Omnia Mounir Fathallah, eds. (2008), a series of papers from a conference on the same topic.
A mention of Umar directing the burning of the library is first found in the 12th-century writings of Abdul al-Latif al-Baghdadi. Ibn al-Qifti, who visited Cairo in 1200, writes of the incident in his History of Learned Men (Ta'rikh al-hukama), and his story was repeated a few years later by Bar-Hebraeus. In other words, despite a rich literary tradition, half a millennium passed when no source, whether Christian or Muslim or Jewish, from anywhere within the Arab or Byzantine or Persian worlds, makes any reference to the destruction of the world-famous library that supposedly occurred in 642. That is, none until it surfaces in al-Qifti, for whom it was politically expedient.
The library had already suffered. A good part of its collection was destroyed in 47 BC, and another in 273 AD, and probably more in 391 (although blaming Patriarch Theophilus seems to be an equally scurrilous accusation, considering his real target was the Temple of Serapis in another part of the city). It's possible that the story is a fabrication; it's possible that Amr burned a different library, perhaps that of a monastery, that became conflated with the Great Library; or perhaps Amr did burn the Great Library— but by that time, itw as a library great only in name.