I like Sera. (And Viv.)
I think the reasons why she is hated are stated pretty well, though. Her breakup with the Dalish Warden who keeps/develips the belief in the Dalish gods is harsh, but honestly, breaking up for religious reasons makes sense- happens aaallll the time. To me, her reaction to the Solas romancing Dalish is worse: the snarky line about the elf having to have the elf for the babies to mean something (really?- you think my character is just a brood mare?!), and then top that off with the scene if you get your blood writings remove and she's basically like "HAH YOU WERE ALL WRONG" while your Inquisitor is standing there all shamed and possibly heartbroken with a broken expression on her face.
And, yeah, despite brutally murdering tons of people in these games, I found her beatdown of that (fairly horrible, from what we know) dude honestly pretty scary. All three protagonists can do worse things (I find Hawke selling out his little sister to Meredith while wearing a stupid smirk one of the worst things in game, even if people say Hawke can't do 'evil stuff'), definitely, but it's not usually as detailed as Sera completely beating the crap out of some dude while your Inquisitor (can) plead with her to stop. Murder knife, throw it, splirt of blood, over. This scene shows a detailed beatdown, which is a bit unusual.
...My first character was actually a Dalish romancing Solas, but as long as they didn't go in to personal beliefs, they got along fine. That makes sense to me: I have a ton of friends who I like, but who I would in no circumstance want to discuss politics/religion/other similar stuff with. My second character, I actually tried to be an ******* with to *everyone* (save for Cass and Viv, who were his besties)- somehow, I still managed to get her friendship roof scene (possibly because he used his noble connections to recruit the ******* she can beat down?), and despite him trying to be rude as he could be (COOKIES SUCK), she still apparently adored him. (Blackwall, at least, properly hated him from day one, and never did his personal quest.) My third character was a Qunari who romanced her, and then I really did start to like Sera (who was mostly a target of my indifference before). Sera is childish, abraisive, terrified of things she doesn't understand- and yet surprisingly good hearted and steadfast in the end.
I don't think she's one of Bioware's most likable characters, but I do find her very understandable: she's in over her head, she lashes out, she isn't willing to look past her stubborn beliefs and she can be downright nasty to people she's not fond of. This is more of a case of 'If we were friends in real life, I'd throw you in a lake' (but, honestly, most of the DA:I character's I'd throw in a lake), 'but as this is fiction, I think you are very well written and interesting and facinating in your own way'.
...Also, her finally calling Cole 'him' is a moment of Heartwarming and Squee, and her diary (especially if romanced!) is adorable. So, points.