Eugene eventually fixes himself up and starts sprouting some gray hairs, but in his earlier appearances on the show, he had a mullet to end all mullets. An apocalypse may have decimated the world and all norms about physical appearance, so you could say it's okay, but ... had Eugene's hairstyle died with the old world, it's more than likely that very few survivors would have complained, or even thought about mullets ever again.
That's not to say McDermitt can't pull it off, because he absolutely does — and it absolutely fits Eugene as a character. The actor doesn't wear a wig, either: he committed to the mullet for all of his character's early appearances. He also had to dye his hair black, because in real life, his hair is strawberry blond, and he tends to wear it short.
If you stood McDermitt and Eugene next to one another, you could easily call them twins ... all but for the hair. It makes enough of a difference that, "twins" or not, they give off completely different vibes.
There's also Eugene's comics appearance to consider. Illustrated by Charlie Adlard (who took over for Moore after he left early in the series' run), the character is perhaps 10-15 years older than McDermitt. Adlard depicted Eugene with a mullet before, but the character was also seen with a braided ponytail, as well as with aviator goggles strapped to his forehead. Put this Eugene next to McDermitt, or the show version, and the resemblance is hardly there.