Realistically, nothing.
But, let's entertain just a handful of hypotheticals.
Retribution. I live near some real wackos. They're proud to intimidate minorities out of town. They're also violent. I witnessed a neighbor get into a fist-fight with another over the placement of a mailbox. The victim called the police and I was a witness. No charges were filed. However, a couple days later, the aggressor and his buddies cut the victim off, dragged him out of his car and beat him so badly that he needed to be airlifted to the hospital - over a mailbox. I don't want these rednecks knowing that I'm a liberal athiest. And getting mail or visits from a political party could jeapardize my current neutral wallflower status.
My political alliegence could hurt me at work. Not from my employer, but rather my clients. I work in mental health and need to be as neutral as possible, or act as if I'm taking a side with my client to deescalate a situation. This allows clients to trust me. But, were my political affiliations openly known, then it would change that perception of neutrality and could hurt me.
It just irritates me. I don't like the state knowing my political stance, because then I'm just a statistic to be jerrymandered about. I'd rather be a quetion mark that my politicians need to consider and consider reasonably.
Political acceptance. I tend to be politically active. I don't march, nor do I hold banners. But, I do write my state and federal representatives and senators frequently about issues. I believe that political neutrality helps. I don't appear as another member of the choir, nor am I outright dismissed. I doubt that my leaders are checking to see if I'm on their list or not, but it's possible.
Chances of anything like this ever happening are slim. But, it aggravates me that it could, so I'd rather be politically private.