It's entirely possible, for example, that religious belief has had a positive influence on believers lives & society, but skepticism demands the entire structure be questioned, doubted, and IMO rejected, despite any positive value.
Huh? Questioned and doubted, sure; but rejected? Skepticism demands only that conclusions and decisions be based on evaluating the evidence (that's the questioning) and doubted if they haven't been (that's the doubt). What are the positive influences, and what negative influences must those positive ones be weighed against? That's a question that skeptics should and do ask.
"Religious belief" has multiple facets, most of which fall under the three general categories of narratives, practices, and experiences. Whether or not some or all the narratives are true is not the sole determiner of whether the practices or experiences have net positive or negative value.
For sure, there's plenty of uncritical thinking on both sides. Claiming unbounded "positive value" based solely on an unverifiable claim of the truth of a narrative (e.g. Pascal's Wager) is just as much an example as claiming that no positive value is possible at all if the narrative is false (which would reject all positive value for fiction, fables, legends, parables, etc.) Neither of those demonstrate skepticism, though.