In her elegy to the Reverend George Whitefield, African-American poet Phillis Wheatley expresses her admiration for the Anglican minister and laments his passing. Lines five and six communicate, as you say, "the egalitarian nature of the Great Awakening."
"Thy sermons in unequalled accents flowed,
And every bosom with devotion glowed;"
Wheatley observes that Whitefield had no equal in the pulpit and that everyone who heard his sermons was devoted to him and God. The Great Awakening, a religious revival movement in the American colonies which Whitefield was involved in the 1740's, sought to bring all people to the church; this egalitarian spirit was much different than the exclusionary stance the Puritans had taken in earlier years in the northern colonies.
It may well be that Phillis Wheatley, a slave in a Boston home, was especially impressed by a man who welcomed African-American slaves into the church and preached that God did not discriminate. Some credit Whitefield with establishing African-American Christianity.