Reading some of the comments on here, I'm inclined to think that some people are over-reacting an others are paranoid that these animals will simply 'overthrow' us
Such sentiments could born out of a variety of reasons:
1) A Collective Guilty Conscience
With people who protect the rights of animals, from those who organize and help at homes, shelters, and other places that house stray animals, and treat them as equals surely don't seem likely to encourage the wrath of potential animal overlords. If you have a pet, don't they always check to see if they can trust someone, but will warm up to someone they believe they can trust? Monkeys are peaceful creatures, as opposed to chimpanzee's which are known to be incredibly territorial and violent, if animals would be "more like people" then surely they could see there are people who aren't in need of being overthrown.
2) Science Fiction Depiction
In the Planet of the Apes movies, the Apes are said to have seized control because humans treated them badly, I would point you to number one, which can completely prevent this step by showing through example that humans are not evil, and do not need to be 'overthrown'
3) Fear of Inferiority
A lion has retractable claws, can see in the dark, weighs far more than the average human and can exert far more force than we can. Evolutionarily speaking, a lion is physically superior to us in almost every way, apart from a lack of opposable thumbs. Monkeys are an obvious choice because we can see that they may come to look like us, and act like us, and because they already have thumbs. It would take centuries if not millennia for other species to reach that evolutionary milestone.
4) Animals are not Overlords because they May Have Better Things to do
The idea that as soon as an animal is intelligent it's thoughts are "enslave the human race" is a bit of really eager thinking, we, as a species are naturally violent, or have been conditioned to see change as potentially violent and catastrophic, but an animal will only attack if there's a need for survival, if nature demands it, or if it's provoked. The idea that a lion man's first instinct as a 'cub' is to grab an automatic weapon and mow down 100,000 people is a bit excessive and unrealistic.
The idea that animals want to take over the human race is a very strange way of thinking, as animals are already intelligent to a certain degree, cats are supposedly able to understand up to 200 basic words, they can communicate their feelings using body language and tone of voice, and have personalities of their own, if anything, simply boosting their intelligence won't make them bloodthirsty dominant slave masters, and movies like the Planet of the Apes automatically assume that a human resistance and quarantine would be ineffectual. Not taking into account the fact that there are many solutions were an animal uprising to occur. But if we continue to think animals as beneath us, then don't we act in a way that they'd be overthrowing humans that did not see them as equal, but slavering beasts to be abused and mistreated as they pleased? It becomes a question of whether we're ready, and if we're equating genetic research with potential Armageddon, then we're clearly not ready for co-existence with anything at all.