To my eye, both sentences parse properly without obvious error. In everyday (American) English you won't have any issues with being understood correctly in situations like you are describing, nor will anyone complain about your using the preterite. Many, perhaps most, native English speakers will not notice if you use one form or the other.
That said, I personally prefer using the past perfect tense in these cases. Modifying the second example in your post
She [had never seen] a bear before she moved to Alaska.
indicates a state which persisted for an unspecified amount of time, and that state ended with a particular event. Conversely, the preterite
She never saw a bear before she moved to Alaska.
suggests a particular event at a particular time. It is a little bit odd with an extended but undefined time period in which the event did not ever occur, but there is no confusion nor any ambiguity of meaning.
If the time period were better defined the preterite form would sound modestly more natural to me, but not so much so that I would say you definitely should use one form over the other:
In the ten years before she moved to Alaska, she never saw a bear.
<p>In the ten years before she moved to Alaska, she had never seen a bear.</p>
So, which of two sentences given below would you use?
I had thought god didn't exist until a few days ago when you showed persuaded me into believing in the existence of god.
I thought god didn't exist until a few days ago when you showed persuaded me into believing in the existence of god.
– lekon chekon Jun 15 '16 at 08:04