To my understanding, certainly from my experience, for small scale hobbyist use, if you're soldering with wire solder and an iron, or with applying paste solder then using either an iron tip or precisely aimed hot air gun to heat it, you'll probably get away with ignoring the moisture warnings so long as you keep parts in the bag and reseal it with some wrappings of tape between uses. Things would be more problemtic at industrial scale, and with any soldering process where the whole board gets heated during soldering.
Also, I think some sellers might just stock that one sort of bag with moisture warnings as the packaging in which they'll ship anything ESD sensitive. They might not bother to have any bag in stock for ESD protection but which doesn't carry the moisture warning. That said, I think some parts which are moisture sensitive don't warn so on their datasheets. I hear all SMD LEDs are strongly moisture sensitive, but I've often seeen datasheets for specific models of them which make no mention of moisture.