However, there is nothing in the law that prevents them from trying to convince your employer to terminate your employment. It is up to your employer whether to listen or not.
CBG is quite right... assuming of course that your parents effort are legal. A prospect that will depend on very specific facts.
If their efforts to convince the employer are slanderous, libelous, otherwise defamatory, etc., that would be illegal, and to which you would have some civil redress.
If the actions of the parents rise to harassment or abuse this attempt to have you fired may be a criminal matter.
If the situation rises to such levels an order of protection is possible, along with other redress.
At the very least, if your parents do this their conduct is
potentially economic abuse, conduct intended to stop a victim from earning a living or being financially independent from the person victimizing them... a crime of family law domestic violence. (You do not stop being their child even when you are no longer a minor.)
Nebraska law defines criminal harassment as (a) Harass means to engage in a knowing and willful course of conduct directed at a specific person which seriously terrifies, threatens, or intimidates the person and which serves no legitimate purpose;
You do not need to be threated with bodily harm for matters to be harassment. Many people, including posters on this board will imply a threat of violence is required for criminal harassment.
They don't even need to call your job for it to be harassment, it would be enough for them to repeatedly tell you they will.