Prison has its own social hierarchy and moral code, and certain offenses sit at the bottom of it regardless of how the outside world views them. Crimes against women and children consistently rank among the most looked down upon within the inmate population.
Domestic violence cases vary in how they are received depending on the specific circumstances. A situation involving a mutual altercation between adults is viewed differently from one involving severe abuse, serious injury, or children being present. The inmate population makes its own assessments based on whatever information circulates about a person's case, and that information does travel through a facility faster than most new inmates expect.
The practical risk level depends on several factors. The nature and severity of the underlying offense, the security level of the facility, the specific dynamics of the housing unit, and how the individual carries himself from day one all affect whether problems materialize. Inmates who are discreet about their charges, keep to themselves, show respect across the board, and avoid drawing attention to themselves generally have fewer problems than those who are open about their cases or who come in with a confrontational attitude.
The most protective thing someone in this situation can do is not volunteer information about their charge to other inmates. The question of what someone is in for comes up early in most prison environments. A vague answer or a redirect is safer than specifics that could make someone a target.
If harassment or threats do materialize, the appropriate response is to report it to a counselor and request protective custody rather than attempting to handle it in a way that leads to additional charges.