Graphic artists get recruited by all kinds of businesses and organisations. That you worked for Vegan World doesn't mean you're vegan, that you worked for James Cybersecuriry doesn't mean you know about tech.
Its irrelevant to the next job, what motivated you to join your past one.,within pretty wide limits. "I worked for the KKK" might not go down well, but the fact you got employed by some political body -
"They were an employer, and my personal politics don't enter into the workplace. They could as easily been Republican as Democrat (US version), Labour or Conservative (UK version), Indie or Green. I was employed to do their graphic design and did it well. I would bring the same professionalism and care and skill, to my next employer, whoever they may be."
If they probe, hold tight on it being irrelevant and a policy of yours, as a graphic professional, never to bring or express your personal views at the workplace. Some will shake heads but quite possibly a lot will nod and appreciate.
If they found out you are supportive of that party, somehow, then at a pinch, you can still be dismissive. "I support them. But that's personal, not workplace, I don't bring my personal views into the workplace and I won't be doing so here." But try to avoid it, and move the conversation on instead, before they ask that.
If needed, and comfortable, also say that in your free text in your resume/CV if you do e-applications in some abbreviated form, so it doesn't look like making a point.