Post apocalyptic community of Amazons who hate patriarchy. The class of ruling women treat men as slaves and as baby makers. They worship 4 gods. One is named Ibrim. A member is sent out on a mission to seek the gods. She comes across Mt. Rushmore and realizes to her horror that their gods were men. Ibrim is Abraham Lincoln.
Meg becomes a woman and does not want to become a warrior, or a breeder or a worker. Instead she embarks on the titular pilgrimage.
She thought suddenly of their gods. Of austere Jarj, their leader, of lean Ibrim and taciturn Taamuz. Of far-seeing Tehdi, she whose laughter echoes in the roaring summer thunders.
And she discovers they are men:
She had glimpsed that-which-was-not-to-be-seen! The Gods themselves, standing in omnipotent majesty, upon the crest of the towering rock.
For tremulous moments Meg knelt there, whispering the ritual prayers of appeasement. At any moment she expected to hear the thunderous voice of Tedhi, or to feel upon her shoulder the judicial hand of Jarg. But there came no sound but the frenzied beating of her own heart, of the soft stirring of dull grasses, of the wind touching the grim rocks.
And she lifted her head and looked once more....
It was they! A race recollection, deeper and more sure than her own halting memory told her at once that she had not erred. This was, indeed, the Place of the Gods. And these were the Gods she faced—stem, implacable, everlasting. Carven in eternal rock by the hands of those long ago.
Here they were; the Great Four. Jarg and Taamuz, with ringletted curls framing their stem, judicial faces. Sad Ibrim, lean of cheek and hollow of eye. And far-seeing Tedhi, whose eyes were concealed behind the giant telescopes. Whose lips, even now, were peeled back as though to loose a peal of his thunderous laughter.
And the Secret?
But even as the question leaped to her mind, it had its answer. Suddenly Meg knew that there was no visitation to be made upon her here. There would be no circle of singing virgins, no communication from those great stone lips. For the Secret which the Mother had hinted... the Secret which the Clanswomen must not know... was a secret Daiv had confided to her during those long marches of the pilgrimage.
The Gods —were Men!
“The Gods — great Jarg and solemn Taamuz, lean Ibrim and far-seeing Tedhi — are not Women like ourselves. Deep in the shadowed grottoes of far ’Kota I have looked upon them; I have seen their faces strong and fine, covered with the crisp man-hair. The Gods of the Ancients, Beth — are Men!” Chuck glanced at Duane curiously. “She’s seen the gods, Steve?”
Steve nodded. “So have we, Chuck — in the modeling. I’m not surprised these women worshipped their statues. They must be impressive to a civilization so backward as this. In the Black Hills . . . the side of a mountain carven in a gigantic work of art . . . don’t you remember? George . . . Thomas . . . Teddy . . . Abraham. . .
“Mount Rushmore!” gasped Chuck. “That is the ‘Place of the Gods’!”
This is very likely the story Pilgrimage by Nelson Slade Bond. Originally published in a 1939 issue of Amazing Stories, it seems to match the details remembered exactly.
The story centres around the coming of age of a girl in a matriarchal society where men are only kept as servants, in a future where much knowledge has been lost.
Meg has to undertake a journey to the place of the 4 "Gods" of the society as part of the coming of age ritual. She journeys to what we would know as Mount Rushmore to discover that the gods have the resemblance of men.
The quote below is from the linked page and as mentioned in the question Abraham Lincoln is known as Ibrim.
Here, she will learn the final secret of the four strong female deities: “the Great Four. Stern Jarg and mighty Taamuz, with ringletted curls framing their stern, judicial faces; sad Ibrim, lean of cheek and hollow of eyes; far-seeing Tedhi, whose eyes were concealed behind the giant telescopes; whose lips, even now, were peeled back as though to loose the dreadful laughter.” It is a truth kept from the Clan for many generations.