Twilight and Mormonism
This whole series seems to be infused with Mormonism, which is understandable considering the author. Edward is described physically as Joseph Smith; Carlisle is in many ways portrayed as God; even Rosalie Hale is quite obviously a reference to Smith's first wife, Emma Hale. Similarly, the morals in the story are largely Mormon: No sex before marriage, when it happens no attempts are made at birth-control. Free choice only exists so a person can choose to be virtuous by choosing to suffer, which Bella and the Cullens do continuously throughout; Bella by moving to Forks and taking on all kinds of domestic chores afterwards, the Cullens by abstaining from human blood which weakens them and causes them to always be longing for it.
When Bella becomes a vampire, she does it by dying - and being reborn as a Saint, finally equal to her angel Edward. The sparkle-in-sunlight effect is comparable to a body-sized halo, such as saints are seen to have in certain paintings. Of course, once one is a vampire one is practically omnipotent - there is nothing you can't do - like a God.
Meyer herself has admitted to being influenced by Mormonism in her writings, although she denies intending it as propaganda.
However, when Bella sees Edward's "phase" of murdering people in his vampire youth as "natural", it is more reminiscent of Meyer's views on youthful mistakes - like giving Jacob a free pass on his sexual assaults and pedophilia - than of anything an actual person who isn't a sociopath would say.
How becoming a vampire affects youThe LiveJournal site Das Sporking has a rather interesting analysis of how going from human to vampire changes a person and enhances their core personality traits - just not the way Meyer intended. Check it out here, starting about half-way down the page.
But to summarize: Turning into a vampire seems to solidify and intensify your beliefs to the point that you treat them as reality no matter what the actual reality is, and your wants turn into needs and you feel entitled to them no matter what. Also due to the first point you are unable to reconsider them in any way. Also it enhances more than your core personality traits it has this effect on everything you are.
Why The Series Is So Widely Loathed(This is going to crib heavily from Lindsay Ellis.) While Twilight was critically panned and undeniably flawed, much media is, but Twilight is unique in the level of hate it gets. While it may be cliched and unrealistic, there are many wildly successful and critically disdained works that are (the Transformers Film Series comes to mind.)
So what's the difference? Transformers is based on male Wish Fulfillment- getting hot girls, seeing robots beat each other to pulp, etc. By contrast Twilight is based around female Wish Fulfillment- being rescued by a super-rich, super-handsome, super-powerful sparkly vampire. As such,it is widely seen as making Bella seem passive and the narrative sexist- when ultimately, the misogyny may be (almost certainly unintentionally) with the person criticising it for being sexist, You Bastard!