Is it bad practice to study or reference the work of an academic who has fallen from grace?
No, it's generally not a bad practice. For a closely related question, see How does it affect the treatment of a mathematician's results, if that mathematician was a Nazi?.
Should individuals publishing work in his field avoid referencing his texts or published research?
His published research:
for sure no, not avoid references to his research; the linked question covers this well.
As for his textbooks:
Most often one is not forced to reference any particular text, as there are other texts that do the same. (Perhaps "there are other texts that do the same" ought to be the definition of a text rather than a research article or monograph, but there are exceptions to this definition.) I think personal preferences can and do come in when choosing which text to reference: for instance, I would be happier to reference a text that is freely available online, or if I don't like (academically speaking) a text generally then I might try to replace a citation to it by a citation somewhere else, even if that's a little trouble. (I remember doing that recently in a joint paper: a coauthor cited a text I didn't like. I got him to (find and) cite another one instead!) But if Dr. Fallen's text is the unique source for something, you must cite it, and if you unambiguously feel that it's the best source, you probably should cite it.
As for your studying: I see no argument whatsoever against studying the good text of a bad person. In fact, "bad person" is a kind of reification. Everyone does good things and bad things; when we say someone is a "bad person," we mean that our evaluation of their actions (that we know of) is weighted towards the bad. But avoiding or trying to nullify the good actions of a bad person is...bad. We should encourage, reward and make use of the good behavior in everyone, right?
I do have one proviso: you may not want to financially support Dr. Fallen, for instance if you suspect that financial support would somehow abet his reprehensible activities. So you may well not want to buy his book if you haven't already. If you feel that citing Dr. Fallen's text in a situation where you could also cite another (both are secondary sources) could induce others to financially support him, then maybe that's an ethical reason for choosing a different citation even if you personally think Dr. Fallen's text explains it better: this is a bit of an unlikely edge case, I think.
Unless that fall from grace precludes being able to take their science seriously (see: Andrew Wakefield), there is no reason to avoid their work. As other people have mentioned, a citation is not a personal endorsement of an individual as a good and decent human being. It is a pointer to a body of scientific work.
If Einstein was a warmongering Nazi, would his scientific discoveries become something less than they are now?
If the book is helping you, you should continue using it.