Can stainless steel or galvinized screws be used indoors on non-pressure treated wood?
Stainless steel is more brittle than the steel commonly used for screws. In some cases I have twisted off long ss screws. This may be a critical deficiency in some applications.

I use stainless steel exclusively for installing grab bars in showers. These are ss screws which come with the bars. In dry situations I use whatever I have except never drywall screws.

I once tried to use long ss screws to secure an owl box to the trunk of an oak tree and I twisted off the screws. I then used deck screws with no problem. 

BoltDepot


  Stainless steel is an alloy of low carbon steel and chromium for
  enhanced corrosion characteristics. Stainless steel is highly
  corrosion resistant for the price. Because the anti-corrosive
  properties are inherent to the metal, it will not lose this resistance
  if scratched during installation or use.
  
  It is a common misconception that stainless steel is stronger than
  regular steel. In fact, due to their low carbon content, many
  stainless steel alloys cannot be hardened through heat treatment.
  Therefore, when compared to regular steel, the stainless alloys used
  in bolts are slightly stronger than an un-hardened (grade 2) steel but
  significantly weaker than hardened steel fasteners. Unless great care
  is taken, stainless fasteners are susceptible to seizing up during
  installation, a phenomenon known as galling.
  
  Most stainless steel fasteners are much less magnetic than regular
  steel fasteners though some grades will be slightly magnetic.