I was told by a Muslim that the category of "people of the book" in Islam, which includes Jews and Muslims, has been considered at some points in history to include Hindus as well. What is the view of modern Islam on this issue?
Technically, the People of the Book are defined as those people who were given a revealed Scripture from God. That is who is referred to by the term. The thing is though, that certain rulings that apply to People of the Book can be extended to other faiths as well and some can't, depending on the context of the ruling. So while other faith communities may not fall under the category, the ruling that applies to them might.
No Hindus are not considered people of book
Please see the link below for details people of book according to islaam
The three types of adherents to faiths that the Qur'an mentions as people of the book are the Jews, Sabians, Magians and Christians
No, only Jews and Christians and their sub-sects are People of the Book, and no religion other than them, since only two groups were given the Scripture:
أن تقولوا إنما أنزل الكتاب على طائفتين من قبلنا وإن كنا عن دراستهم لغافلين
[We revealed it] lest you say, "The Scripture was only sent down to two groups before us, but we were of their study unaware,"
وفي ذلك دليل على أن أهل الكتاب هم اليهود والنصارى
This [verse] is evidence that the People of the Book are only Jews and Christians
فإن أهل الكتاب من الكفار هم اليهود والنصارى لقوله تعالى : أن تقولوا إنما أنزل الكتاب على طائفتين من قبلنا فلو كان المجوس أو غيرهم من أهل الشرك من أهل الكتاب لكانوا ثلاث طوائف ، وقد اقتضت الآية أن أهل الكتاب طائفتان
The people of the book among the disbelievers are the Jews and the Christians, as Allah says [this verse], if the Magians and others from the people of shirk were from the people of the Book then there would be three groups whereas the verse requires that there be two groups
Hindus, because of their idolatry and polytheism, are apparently closer to the Mushrikeen of Arabia rather than to the Ahlul Kitab.