This is easy, but first a clarification. Chimps share 98% of their genome with humans. The actual number of genes are still estimates.
Chimps are very human-like, but they won't vote. However, chimps are not liberals. They don't talk about their feelings. They're very concerned about their freedoms and don't like big government. They're too smart to be liberals.
"Yeah, we're smart....
We got opposible thumbs on our FEET, too!
I guess we've further along the 'toolusing' line than you mere humans."
But they whine like liberals, and since they have neither permanent addresses, nor American citizenship, nor driver's licences, they qualify to vote under Motor Voter.