In prison, it's a foregone conclusion that whatever you were charged with will become public knowledge. Even if nobody leaks information, much of it is public record or in the news. Inmates gossip like crazy due to boredom and how tense the social situation is, and the only way to fly under the radar is to be someone nobody gives a shit about as well as insanely lucky. That said, there's a very real chance it won't even matter.
How sophisticated and effective prison systems are varies wildly from state to state (if you are going to commit a felony DO NOT do it in Mississippi) but most of them do make a good faith effort to split up different types of offender so as to minimize violence. Sex offenders getting attacked/killed does happen, but in most cases they will be in lower security classifications, far away from the hardened killers. If half the people in a unit are there for sex crimes, is a random drug-runner really going to add twenty years to their sentence to make a philosophical point?
Low-security sex offenders misbehaving until they get thrown into a rougher unit can happen, but in many cases they would be put into seg or a unit which specialized in dealing with that sort of inmate. There is nothing so corrupt or brutal that prison staff somewhere would not do it, but the general incentive (at least for the higher-ups) is to avoid those situations as much as possible, and people tend to wildly overestimate how often this happens.
Also, there are lower-security mental health units which are basically old-school asylums hidden inside prisons, where there are people who cannot be let into society but pose little physical risk to staff. As Virginia is a mid-sized state with multiple blue cities, I'm going to go out on a limb and assume it has a few of these, and if Chris faces a serious prison term, it's pretty likely he will end up there sooner or later.
The US penal system is a massive, byzantine system with little coherence or standardization, so making any predictions about a system you have not personally interacted with is inherently limited, but the people who expect Chris to get eaten alive by gangbangers have been watching too many movies.