The Master Summoner Archtype of Summoner is unable to take the Extra Summons feat.
Master Summoner augments the Summon Monster ability, but does not replace it, so I believe a Master Summoner should still be able to take this feat.
Daniel, when you use terms, please make sure you use them correctly. Paizo's terms and your terms are not meshing. The Summon Mastery contradicts what your saying "This ability replaces the summoner’s normal
summon monster I ability and shield ally."
Lucky for you the requirement isn't actually Summon Monster Class Feature of the Summoner, it is the ability to Cast Summon Monster as an SLA.