While being friends with a coworker doesnt mean you can be fired from your job, you could get fired if your relationship causes a disruption at work. Rather than risk losing a job for your relationship, keep all of your personal relationships out of the workplace, even if they are with coworkers.

Is it illegal to have a relationship with a coworker?

Under US law, dating a coworker is not illegal, and any rules or restrictions enforced by your employer regarding fraternization and dating people at work are employer-specific, rather than mandated in law.