It has recently come to my attention that a renowned scholar in my field whose academic journals have been highly influential in my area of research has recently been charged with child pornography. Is it possible to separate the scholar from their work? And will my thesis research, in turn, be judged for referencing the work?
Of course it is appropriate. Why not? They did relevant work, so you have to cite them. With citing, you do your duty -- you are in no way saying you "like" the cited persons.
Of course, I am assuming that their research is sound and is not somehow influenced by the child pornography. It was a different case if there were problems with the research.
On the other hand, not citing them could get you into big (or small) trouble.
I think that in almost every field you can separate the work from the person who did it. Many people in the history of science and mathematics, at least, have turned out to have "feet of clay." You aren't tainted because you use someone's work.
The only exception I can think of is if the charge of misconduct is somehow related to the research - unlikely.
The Unabomber was a prize-winning mathematician before he turned evil. His mathematical work doesn't disappear from history.
I agree completely with guest2's answer. I'll add this: The author has only been charged. He/She hasn't been convicted.
Presumption of innocence - i.e. the idea that people are innocent until proven guilty - is one of the most sacred principles of the criminal justice system. Even if someone disapproves of you citing a child pornographer, they can't really fault you for doing so before the author is convicted.
To add another perspective to this, you even knowing of this author’s (alleged) crimes is a great coincidence:
A considerable amount of criminals is never caught. In particular for ownership of child pornography, I would expect the dark figures to be so high that I have likely cited somebody guilty of it.
In many countries, e.g., Germany, privacy laws or at least codices of press, police, etc. forbid publishing the name of a criminal for protection of their rights, allowing rehabilitation, etc. Names are usually made public only if the person in question is in public spotlight anyway (e.g., in this case of a member of parliament) or the case itself is of extraordinary public or historic interest (such as this one, and even there, it took a while). So, you probably only know about the crimes of the author in question because they were in a country with another attitude to privacy, were considered in the public spotlight anyway, or information leaked out somehow.
You either had to investigate this author or this was a widely available knowledge in your field, which is also something you cannot assume to happen in every case – at least I do not investigate whether there is some public criminal track record of every person I cite.
So, what makes that specific author different from authors whose crimes you never get to know?
And even if we presume that something is different, what should the scientific community do about it? Reiterate the author’s entire work and publish it again, so it can be cited? Is every convicted criminal’s work free game for plagiarism? (This becomes particularly absurd in fields like pure math, where a paper can be fully self-contained.)
The only exception from all of this I can see is if the author’s research can be expected to be biased due to pedophilia. But then it’s upon the scientific community or the respective journals to judge this and retract or annotate the respective publications.
Others calling this an "ad hominem fallacy" or saying you must "separate the scholar from their work" are wrong. In a system where citation is the currency that fuels careers, you can't separate them; any resolution of this dilemma must acknowledge and attempt to mitigate the fact that the author cited does usually benefit from citations. This is particularly true in cases where the author is still alive and still has a career, but in the case of hateful ideologies (e.g. Nazi works), there is also the aspect of citation benefiting the ideology that lives on past the author.
Now, how do you do that? It's hard, and academia doesn't have good solutions right now. Fixing the whole academic publishing system and citation economy is related, but not really something you can wait on. From an academic integrity standpoing, you do have an obligation to accurately cite work you used, were influenced by, or built on. But if this person is a "renowned scholar" and "highly influential" in his area of research, there's also a good chance that he's going to get off with a slap on the wrist, partly due to the justice system and academic community considering him "too big to fail" or considering the "value of his work" too important to jeopardize by ostracizing him.
Sadly, I don't have any good answers for how to fix this or even avoid being complicit in it. But I do think it's worth saying that the people who are telling you it's not an issue are morally bankrupt.
On a related note, the Unabomber was once cited with a footnote "Better known for other work."