Are Orthodox Jews allowed to read secular books, and if not, why not?

It appears not, on the whole according to 'ask the Rabbi' except on the Sabbath and not certain things that most religions would ban anyway.

https://www.yeshiva.co/ask/6501

The Rabbi suggests that strictly observant Jews are only prohibited from reading secular material on the Sabbath and on holy days, though it is considered sinful at any time to read the sort of material that a religious Christian or Muslim would also shun. The Jewish people I work with have as many secular interests and hobbies as anyone else.

The ultra orthodox chasidim do seem to avoid anything which takes away time that might be spent on biblical study, but I think this can be said of the most fundamental of Christians and others as well.

There is a great diversity in rabbinic thought on this subject so it depends which rabbi you ask.

The following are the guidelines I learned from Orthodox rabbis here in Jerusalem.

Any secular pure science subjects are generally permissible, even on Shabbos. Shabbos is after all a time to appreciate the creation. The theory of evolution is frowned upon in many of the most orthodox circles but descriptive empirical science (and math) without any speculation is fine. History, geography and other factual material is also fine, even on Shabbos though the Torah Scholar is encouraged to devote as much of his time to learning as possible. Many great rabbis in history were conversant with the sciences and clearly devoted much time to their study, particularly the Rambam.

Literature is contraversial in other ways because of content deemed undesirable for the devout, particularly lack of modesty. Secular literature is generally banned on Shabbos and it is very debateable whether it is allowed during the week though no rabbinical authority I know has banned all secular literature. Each book and author has to be taken on their own merits.

Though it must be added that according to the halachah (strict Jewish religious law), any reading material is permisable. Not just to read, but also for singing purposes (unless one sings religious texts of other religions at actual religious rituals). Yes, we are allowed to read about science, history, philosophy and art on any day of the year. In fact, on some days of the year we are discouraged from spending too much time on religious literature. I have sung Catholic and Protestant masses (never at actual services), and in order to do that I had to become quite familiar with the texts.

However, it should be stated that some literature is discouraged in general or was over time. Rabbi Akiva of Mishnaic times stated that one has no place in the world to come if he's read what he called the "s'farim chitzoniyim" (the "outer books" or apocrypha, he probably meant the Gospels of the New Testament). Over time many Jews have been excommunicated for writing literature that seemed heretical at times (like Baruch/Benedict Spinoza or Anan ben David), and their literature was also banned by the authorities of the day. Many non-musicians here today still don't feel comfortable reading anything that originated in Germany, and certainly not Wagner's librettos (let alone listening to the music).

It's a personal choice. Some very religious Jews I know do not read secular books anytime. Myself, I am a Jew. My personal choice is to read secular books on weekdays but not on Shabbats.