Did Franklin mean to include Irish people in that even if he didn't explicitly mention them? That seems unlikely, because when he wrote that in the 1750s, there was very little anti-Irish sentiment in America, and I'm aware of no evidence that Franklin personally harboured any. Most 18th century Irish Americans were Protestant, and whether or not they technically count as "WASP", they were rarely distinguished from them.
Benjamin Franklin visited Ireland in 1771; I'm aware of no evidence he thought he was visiting a "non-white" country. During his visit, he socialised with the wealthy Protestant establishment, although he saw the poverty of the Irish masses and was struck by it – however, rather than blame it on their race, he attributed their plight to British rule, even later suggesting that without independence, the British would reduce poor Americans to the same extreme poverty that poor Irish endured. Keep in mind that in 18th century Ireland, the Protestant establishment in Dublin viewed themselves as "Irish"; they did not see themselves as a different nationality from Irish Catholics, and would not have agreed that they were a different "race" from them.