Her hobby is regarded by the majority as sick and indecent.
By all means do it, its not illegal, but expect opinion to be against you when you publicly flaunt it.
But you could easily say the same thing about a gay man posting pictures of himself in a gay club kissing another guy. Now, more acceptable but could easily still draw lots of hate on Facebook, but posting a picture like that even 10 years ago would get almost the same response this woman has received.
Ignorant reactions is NOT a valid reason to not share what you do, in fact, it's taught more people the benefits of what she is doing. There are now what dozens of people in this thread that previously didn't know that wild game hunting is actively helping to support conservation of these animals. She doesn't post, these people don't learn that information.
The first gay guy showing the world his kiss with another man on facebook, might attract the same response but also leads to other people being more comfortable to do the same.
Meat eaters enjoy the result of animals being killed. Apparently it's okay to have an animal killed and to enjoy the taste of it, but it's not okay to enjoy killing an animal. Just an arbitrary, meaningless line that people randomly make up, it's okay to like this but horrendous to like that, even though the result is a dead animal in both cases.
Other peoples ignorance is a terrible reason to chose not to post what she did.
Of course, I find the argument that they help conservation rather stupid. They could pay the money purely for the conservation, and the people running these area's could simply tranq the problematic animals(like those who would attack other packs cubs) and transport them to an effectively old animals sanctuary.
Yes one hobby can pay for something good, but they could just as easily pay without the hunting and achieve the same result. It's a shame that it's just not seen as important, because if Bill Gates or someone donated a billion or, 5, we could pretty much world wide have safe places to work on repopulating endangered species.