Is it bad practice to study or reference the work of an academic who has fallen from grace?

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.

I suppose it would depend largely upon the reason for the fall from grace. If the fall was due to falsifying data, that would be a big red flag for serious citation (unless you're pointing out the the conclusions may be false).

It gets more interesting if this involves research that does not meet ethical standards. Mengele did "research", and I suppose there are serious people who can tell you whether any of his results were valid -- but he treated humans as less than human.

Then, of course, are people who fell from grace for reasons that would be considered non-reasons today. I would hope that I don't know too many people who would refuse to cite Turing because of his sexual preferences (though, I confess, I have zero knowledge about how he was regarded in contemporary academic circles, he certainly had detractors in government).

Science is supposed to be about facts. People are very much geared toward good vs evil, and choosing sides.

Bill Cosby, Michael Jackson, Tom Cruise, Jane Fonda, .....

At one time in history each of these people produced some form of art/entertainment that resonated with a large number of people, and then they did something that a large portion of the population found objectionable. Does that make the things they created bad?

Our culture has decided that if someone does something we don't like, we don't like anything they are associated with... until they are dead. Once they are dead we can like their work again. I would argue that it would only be an ethical issue if the work itself were obtained in an unethical way. For instance, if someone tortured a bunch of children just to see how children responded to being tortured.

If the "improper personal conduct and trouble with the law" had potential to make the professor's work questionable, then his work should be excluded from serious consideration.

In many cases, the author's crimes have nothing to do with their research, and if the facts/research/conclusions are true, then by all rights there should be no reason to avoid using it. However, there remains a fear of "crime by association" and it's up to each reader whether they are able to get past the author's or researchers' crime or activity to be able to use the knowledge they wrote about. Sometimes it is the only place to find such information. If that is not the case, some may feel better quoting it from a secondary source in order to avoid the association with the original author.

As an example, in the Numismatic field, there was a researcher who wrote a great encyclopedia that had a ton of research behind it and basically became many people's "bible" on coins. It came to light that the man was a pedophile - many thought this tainted the work he had done, but his proclivities had nothing to do with the cold hard facts of coin mintages and coin design. Seeing as it was the only reference with some information (still to this day), it will be quoted but always with reluctance; the quoter usually finds a way to express their dismay with the author, as if to make clear that they do not condone the author's crimes.

In the end, if the professor's works are factual, then it's up to you; the facts stated won't be any more wrong or right because of what he did in his personal life, but you could also be judged by people who will mentally combine the researcher with the research. So if it matters to you, you may want to gauge your audience's ability to separate the work from the author before citing him or having his books clearly visible on your bookshelf.