Yes, despite the Harambe memes, people do treat animal deaths in general with respect. Memes are not meant to be taken seriously. The joke of the meme has little if anything at all to do with the actual death of the gorilla. In general, animal deaths are treated with great respect and often times more respect than human deaths by certain groups.
It seems that once an animal death becomes "big enough," the internet trolls take over and start producing memes about it. We saw this with Cecil the Lion as well, although it's certainly a bigger deal with Harambe. Clearly it got bad enough that the Cincinnati Zoo requested people stop making jokes about it. Predictably, that did not turn out well for the zoo.
Considering that the Harambe memes are mostly on the side of Harambe and not the Cincinnati Zoo, that is not really the issue here. BUt yes people do give animal deaths the respect they deserve and possibly more respect than they actually deserve. Some people do not, but most do.
Not many people, if any at all, think about the food they're eating in regards to the animal itself. It probably lived a horrible life and killed off horribly. (Some slaughter houses are more humane than others). Nobody batters an eyelid or gives any respect to those animals.
But if we are only talking about animals that are famous or say the gorilla. No. I do not believe so either.
That poor gorilla was killed because a mother could not look after her kid properly even after the kid reportedly said he wanted to jump in with the gorilla multiple times.
To give the animal respect, she should have been charged for something regarding the animals death.
Memes are created for humans too. Tough.
People in general do not treat animal deaths with sufficient respect. Animal life should be respected, and humans should remain cognizant that they are 99% similar genetically to other primates. People should show respect for life itself, regardless of the form. The Cincinnati Zoo is justified in being "not amused" by Harambe memes.