there are various scenarios that could fit into the vague outline that you draw.
one would be that you have an anarchist friend who is accused of something bad and you want to support them even though you think they might have done the bad thing. how do you negotiate that?
another would be that there is someone you agree with even though you don't know them, and you want to support them, and then someone says they did something bad and you don't want to support them if they did do this bad thing, but you do want to support the things that you know about them (ie, the things that made you interested in them in the first place).
there are probably other scenarios but i think starting with those is fine as they are common enough experiences to be worth talking about.
i will start out by saying there is a slogan that could have been made specifically for your question, which is:
solidarity means attack!
ie, if you want to be in solidarity with someone, rather than only focusing on the person who is having hard times, you attack what they were attacking that got them in trouble made them interesting. there are multiple benefits to this strategy, including a de-emphasis on the personal behavior of individuals, and a decentralization of targets for our enemies, etc.
for the more personal conflict, which is actually more what it sounds like you're asking about, it would depend on your relationship with this person. brandon darby is one example of someone who was supported by his friends while he was in the process of snitching people out. so that's one negative example. but there are plenty of daily, mundane examples of people just bailing on friends when the rumors start, which i would argue is at least as bad.
i guess my bottom line, per usual, is that it would depend on context. sigh. ;)
edited briefly to address FA's point...
to say a minute more about the "bailing on friends" thing -- loyalty is important to me (although how to express that loyalty can be complicated, even contradictory), and my understanding of how u.s. culture is moving is away from committed relationships and working things through with friends. so my knee jerk is to emphasize the importance of that.