Is your project something targeted at a general populace? How large the following do you need for it to succeed?
As other commenters mentioned, all the puppies, celebrities, politicians, and everything else you see in the "social media" are precisely the things that work on the vast majority of people. Things that pull on the strings which seem to be directly attached to our most primal instincts.
We all have those instincts, and we're all vulnerable to their exploitation. I think that the majority of people either are not aware or don't really care about being manipulated, as long as they get their fun in the end. If you're going to need the widespread support of tens of thousands or more, then you have no other way than to provide them what they - consciously or not - (came to) expect.
In the infinite diversity of human characters, though, some people are aware of the hidden (in plain sight...) dangers and manipulation techniques and do not want to be targeted by them. They're a tiny minority (again, in my experience), but thanks to the Internet, you can find a number of them. I get the feeling that you're a part of that "crowd" and that you'd be happier targeting just them. Try to think it through. How many people do you really need in your network for the project to succeed? Can you get away with just the ones you share a mindset with? If so, don't bother searching for them in the mainstream. The time you'd spend feeling bad and hesitating to post another puppy can be better spent by looking outside of the puppy-infested hate-laden cesspool of popular opinion.
This may sound elitist, but it's really not. Being in the minority and preferring to stay within that minority is a perfectly natural thing to do. You don't really have to do any coming out if you don't need it. Stay where you feel comfortable, or at least start from there. It could take you more time to accomplish whatever it is you want, but you'll be much happier along the way.
My advice if you actually really need widespread support and fast: hire a firm which will do this for you. As many others said in this thread, they are pros at this game, and you're not going to get results better than them by yourself, even if you ruin your mental health many times over.