As I stated earlier, if one were to "worship the God of Abraham" they would accept Yeshua. In Jesus own words in John 8:56
Your father Abraham rejoiced at the thought of seeing my day; he saw it and was glad.
As I'm sure you are aware, when the unbelieving Jews questioned how Jesus could have seen someone who had been dead longer than Jesus had been alive, Jesus responded "before Abraham was, I am". Jesus makes it clear that "worshipping the God of Abraham" is synonymous with accepting His divinity. A claim which the Jews sought to stone Him for.
As for the ancient peoples known as the Ishmaelites & Hagrites, consider Psalm 83:
1 O God, do not remain silent;
do not turn a deaf ear,
do not stand aloof, O God.
2 See how your enemies growl,
how your foes rear their heads.
3 With cunning they conspire against your people;
they plot against those you cherish.
4 “Come,” they say, “let us destroy them as a nation,
so that Israel’s name is remembered no more.”
5 With one mind they plot together;
they form an alliance against you—
6 the tents of Edom and the Ishmaelites,
of Moab and the Hagrites,
7 Byblos, Ammon and Amalek,
Philistia, with the people of Tyre.
8 Even Assyria has joined them
to reinforce Lot’s descendants.
9 Do to them as you did to Midian,
as you did to Sisera and Jabin at the river Kishon,
10 who perished at Endor
and became like dung on the ground.
11 Make their nobles like Oreb and Zeeb,
all their princes like Zebah and Zalmunna
Did Ishmael & Hagar worship Yahweh? Probably so, considering Hagar cried out to God after they were expelled from Abraham's camp. Did their descendants worship Yahweh? Doubtful, considering Psalm 83 includes them with Ba'al worshipers who were hostile towards the Israelites.
Regardless, Jesus made it abundantly clear (to the point of almost being stoned) that the God of Abraham is the Father & the Son.