Advisor accused of personal misconduct -- what should I do?
There are a few considerations, at least. 

First, is that if you feel personally at risk from the alleged behavior, keep your distance just for your own safety. That is distinct from academic considerations. 

Next, the behavior is alleged, not proved. While it is appropriate to be wary, don't try to judge it yourself unless you have additional information. 

Next, in many cases, I would say most, it is appropriate to distinguish between personal behavior (possibly very bad) and scientific/academic quality of the work. Let me focus on this aspect. 

In the history of academic discourse and advancement, many fine results have been obtained by terrible people. This is true in many fields and over a long period of time. The work done by these people doesn't disappear just because they wound up chastised by their peers, or even arrested and jailed. They get referenced. Historically, you won't find all of the cases as they are often covered up, but some you will and they can be pretty bad. 

My advice, even if the person is guilty, is to separate the person from the work. If the work has merit, then cite it as usual. Focus on the work. 

The question of continuing to work closely with the person is a different one, however, as is the question of the value of letters of recommendation. Some separation of the person from the work is possible here also, but perhaps not as completely. For example, it is probably a mistake to become a defender of the person if it can be interpreted as a defense of the alleged actions. 

Letters of recommendation may be necessary and may be fine as long as the letter focuses on your work and doesn't imply anything more. But you may have to explain, in interviews and such, that you distance yourself from any bad behavior, even if not proved. Here the distinction is between the bad behavior (distance) and the person (neutrality - more or less). However, don't depend solely on letters from someone who has been severely sanctioned either legally or academically.