Sure, people are generalizing that everyone hates Batgirl as DLC. But you're generalizing that everyone is arrogantly stubborn when the reality is; a ton of people wanted Martian Manhunter-- not everyone, but a lot more people wanted him then who we're getting. Any personal distaste for Batgirl that you are seeing is more about people being upset it was Martian Manhunter or a more preferable choice (such as Black Canary) that got left out, and less about Batgirl being the DLC choice.
We know she's extra. We get it. No one is obligated to buy it, but the whole point is that her being the second DLC choice over characters a lot of people (not all people, mind you, since you'll pounce solely on my choice of words being too generalizing) would consider far worthier of DLC. Everyone I know personally felt something equivalent to; 'It sucks Martian Manhunter isn't in the inital roster, but at least he'll surely be DLC,' because that was a logical presumption. So when you see 90 out of 100 people in this forum upset that Batgirl, (and probably Zod, and Scorpion too) are the DLC choices, it is not because they are ungrateful for any extra characters, it's because on average, most people are disappointed with Batgirl being picked over MMH, Red Hood, Poison Ivy, Black Canary when the latter were the majority of DLC requests.
People are also upset that they purchased the season pass with the logical picks in mind (MMH for one), when the DLC choices were clearly from left field, and were hardly requested. I'm relieved I didn't purchase the Season Pass, because I now only plan on buying Lobo. Sure, you could argue that's narrow-minded to completely disregard characters solely because you don't like them even though they may play well or be tournament worthy, but that's how I pick my mains. I don't go by tier, I go with who I like, hence my maining of Black Adam, Hawkgirl, and Sinestro.
I like Batgirl as a character, I really do. I read the comic every month. Does that automatically mean I'm happy she's DLC? Nope. I'd of preferred Martian Manhunter, or Black Manta, or Black Canary, or almost anyone else for that matter.
And again, you're right. She's extra, and I don't have to buy her, so I'm not. In most peoples opinions (which I should point out, "most" being a synonym of "majority"-- a la the most important amount of people), the potential for highly requested characters that didn't make the initial roster, has just been wasted.
EDIT: Also, I don't know, and have never heard a single person that wanted Batgirl to appear in the Nolan trilogy. Now you're generalizing.