To pursue the matter of Sera's reaction further. Her choice of phrasing is interesting here: she says the elven gods can't be real, because there is no room for both them and the Maker. While it's tempting to ask why that is exactly, it leads to the possible break up with an elf inquisitor. Sera hates to be identified as an elf because people tend to use that to excuse all kinds of behaviors. This guy is a douche? Well, he's an elf so you gotta stick with him. Because elves gotta stick together. This guy's ok? Well, he's human, so we don't care. Humans are not our people. You're ok? Well, you're an elf so we humans gotta be wary. Because elves hate humans. Etc. etc.
This 'us against them' mentality is common in both Dalish and city elves. Remember in Origins how some of the Alienage elves looked down on those who integrated into human culture to better their lot in life. Sera tries, and admittedly often fails, not to take race into account. You're either decent or you're not. She has a sort of counter prejudice going on, if you will. Still, she works past it when she gets to know people. Now, the religious point:
Sera is Andrastian while the elf inquisitor is Dalish. Sera is not particularly devout, but she believes. Her ultimatum works on two levels: on the one hand, she is forcing an elf inquisitor to choose between her and their heritage. That's a pretty nasty thing to do, but again her choice of phrase is interesting: there isn't room for both. She believes that the elf inquisitor cannot accept her, Sera, and her Andrastian beliefs as well as their own. (In a contrast to Cassandra who asks if there is room for the Maker among the elven gods very early in the game. Foreshadowing!).
Is it mature of Sera to do this? No.
Is it selfish? Yes.
Is it unreasonable to ask her to take all this information in stride after a lifetime of Chantry doctrine, limited education and life experience? Yes.
It's possible that with time she will be more receptive to the idea, but think about what happens in this game: the sky is torn open, an ancient darkspawn magister shows up, red lyrium and she potentially goes physically into the Fade or at least her friend/lover does (twice). At the point she reaches the temple of Mythal, it's entirely possible that she's just going "please don't add anything more to the mess the world has become. I can't take it."
It's a defensive reaction. She was so utterly unprepared for all that happened and she isn't able to process it. She needs something solid to hold onto. She chooses to cling to her faith (surprising for her, but hey). If her lover can't accept that, well, she breaks up (for an elf at least). It's a strong knee jerk reaction and it sucks to be on the receiving end, but I think Sera just needs more time to process everything. (expanded interaction DLC, Bioware? Pretty please?)
TL;DR: Sera needs a hug.