Just because they're conservative doesn't mean they're publishing falsehoods. Just be on the lookout for bias, which you should for all media.

For example, the oppression of women in Afghanistan is probably being reported on more by conservative sources not because they are against the oppression of women, but because they're hawks who disagreed with leaving Afghanistan, and there's probably some anti-muslim sentiment motivating it as well. Likewise liberal media sources are probably ignoring it because leaving Afghanistan the way America did was largely considered to be a disaster which was finalized under a Democratic administration, and for all their talk of caring about women they did basically abandon half the population of an entire nation. It would probably not help their side of the current election cycle to shine light on the catastrophic fallout of one of Biden's major international policy decisions.