Depends how much you value your job. The notoriety could arguably be a net gain.

Whatever the politics is, I would never hire a designer that would use my site as a platform for his jokes. It is a breach of trust. If you hate him, don't take the job. If you take the job, do it honestly.

The designer has plausible deniability though: "I didn't know who that guy was, I was just looking for photos of clean-cut Republican-looking white people."

Sure. "And we're just firing you because of bad economic situation". Plausible deniability only works when it's plausible.