How important are stainless steel fasteners for redwood?
Primary reason for using stainless fasteners are:


they are corrosion resistant
the have good strength/structural integrity 
they are reasonably inexpensive


Secondary reasons:


they are aesthetically appealing compared to others
they are ROHS compliant


Anyway, the most important thing to note is that galvanized steel is significantly weaker than stainless steel. The corrosion protection is also less durable than stainless.