Tested two familiars today... Lightningsprite Familiar and Drake of Pure Nature Familiar Both put two effects on you. Summon Familiar: (Familiar Name) and the name of the familiar again, with just the name (which is the stat buff) with a gem icon. For whatever reason, you cannot add the stat buff to the list of blocked spells. Both of these ones have rather weak resistance buffs, and I want to have the cosmetic pet without the buff... Currently seems impossible. Can't right click and add the effect to blocked spells, or manually add it.
As an alternate solution, if you have familiar key ring, you can put a different/good buff in the stat slot and click one of the above for the cosmetic. Unsure about the buff blocking.