The Dalish gods only accept elves, whereas Brother Burkel's quest in DAO shows us that the Chantry accepts Dwarves and Sera being an Andrastian shows us that at least one Chantry accepted at least one Elf.
Lots of dwarves and elves can believe in the Maker/Andraste but that's not the same as the Chantry (as an institution) accepting them as equals (because they do not). This is something Leliana wants to change. Plus, Sera is an elf and would have no troubles becoming a devout Dalish if she wanted to (she would just have to believe what they require, same as with the Chantry).
Sera's probably a lot like Leliana in DA:O in that she believes things about the Maker and Andraste that wouldn't be considered correct by the Chantry. This is good enough for her and she can feel accepted for once but a lot of Chantry folk might tell her she's wrong (but Sera doesn't seem to care). Which is interesting....if this interpretation is correct, why would Sera care that the Dalish look down on those that don't 100% adhere to their doctrine but not the Chantry? My guess is that the Chantry does allow for more wiggle room than the Dalish. In the Lothering Chantry, Leliana was mocked by some for her beliefs but wasn't kicked out and she seemed to have a good relationship with the Mother there. The Dalish don't seem to be as forgiving of alternative interpretations of their religious doctrine.
The devout Dalish Inquisitor, on the other hand, would see things differently and still feel threatened by what the Chantry is teaching and as they are seen as an extension of their god's will, the Maker as well. Ultimately, I can understand where Sera is coming from in that scene but I still believe she's unfair to the Dalish Inquisitor. With a Dalish Inquisitor, the issue isn't that you are 100% in support of the Dalish gods existing since the breakup dialog happens even if you tell her that you're unsure what happened at the Mythal temple. You want to play a more agnostic elf that picks the "I'm not sure" dialog line? Still a problem with Sera. She absolutely requires the Dalish Inquisitor (and only her) to say it's completely rubbish. Even a human Inquisitor can get away with saying that they totally believe in what happened at the temple. Regardless of Inquisitor's race, shouldn't that still be a problem with Sera? The Inquisitor is still telling Sera that her religion (the one that is accepting her) might be false and that should be just as problematic, correct?