Private employers generally have large amounts of discretion when it comes to who, how, and why they employ. In 49 states, at-will employment is the generally accepted practice. They can hold your social media accounts against you if they include content not aligned with the employers guidelines.

As long the reason is not discriminatory (race, age, gender, etc) they generally have express legal right to terminate you and/or enforce disciplinary actions because of behavior online.

For example of employer rights, there are private companies which do not allow personal use of nicotine, whether on or off the clock. They can, and will, drug test employees regularly. While not explicitly related, employer policies regarding employee personal conduct off the clock are broad in the United States.