Yes, that Kyne. And eeeh, *waggles hand*, depends on how you want to read it. The religion involved only features Kyne herself and isn't particularly tied to Elder Scrolls lore. It's primarily just a reference meant to build out Taylor's character and, to an extent, her mother's.
The issue that I have with this is that it doesn't
expand Taylor's characterization; instead it makes Taylor into a different Taylor, splitting her into two; the Taylor of Neolithic I through IV, and the Taylor of V and VI; more so in VI than in V.
The Taylor of Neolithic I through IV is methodical and practical, with a
major axe to grind against a lot of people, most especially the people who held power or authority over her who failed her, which is literally all of them. That the Taylor of Neolithic V and VI
is religious at all is jarring. The fact that you have a Taylor with serious listed issues
against Authority figures praising anyone for anything at all - and yes, Gods and Goddesses
are Authority figures -
does not compute with her prior authority issues; this can be reconciled but not without rewriting a good deal of Neolithic I through IV.
The last line of the quote in particular makes the disconnect between the two Taylors even worse, because it was added to the story after the base characterization was done; something done without thinking anything through and without asking yourself the following question: 'Would this character as described so far be like this?'
The rough equivalent for what you've done here is taking a Christian, and showing them praising Christ and God for their good fortune in chapters one through four, but then in chapter five they suddenly praise Zeus for the same sort of things instead, with no explanation or buildup. It's
very weird.
Could the Taylor of I through IV do the same things in parts V and VI? Yes, she'd do almost all of them; she found traces of the Hot Springs in III, she's been searching for local sources of food this entire time, she's wanted more people in the village she's building for at least two parts, etc. She
would have different expressions and expectations about it; different words and reactions.
Would the Taylor of V and VI do the same things as the Taylor of parts I through IV? Probably, but she would have had different reactions and phrasing in a lot of places.
Is it possible to reconcile these two Taylors into one being? I don't think so. Is it possible to rewrite it, so that either the religious aspect is missing or more prevalent, absolutely. It's relatively easy, as the differences aren't
huge; they are the same person in many ways, but they
aren't the same, and that's a key issue in character continuity.
There are also the larger plot implications. Being religious,
especially a minor religion like this Kyne worship is implied to be, would absolutely be something Taylor was bullied for. Likely repeatedly, as she would seek solace in it, and her doing so would be a tool to use against her.
It also can't be a
minor bit of characterization, because of what the existence of 'Kyne' and related Cult/s implies about the wider world; Taylor being some kind of pagan, Wiccan, etc., would require less worldbuilding to support it and have less impact, but not
no impact.
TL;DR: Whether you want to use this bit of characterization or not you'll need to rewrite at least
some of what you've already written to make everything mesh better.