How were the prophets Muslims before the mission of prophet Muhammad peace be upon him?

What is “Islam”?
Islam Is an Arabic word which LITERALLY means “submission”.

Islamically (idiomatically): 
It means Submitting to the One True God, associating no partners with him, and worshipping Him according to the legislations He send with the last prophet at any era.
Accordingly: 
Those who followed Noah, worshipping God alone and applying the legislations sent with Noah (as a last prophet at his time) were Muslims. Also, those who followed Abraham applying the legislations sent to him were Muslims. Same for Jesus followers, were Muslims in the time of Jesus. Also The sons of Israel were Muslims in the time of Moses, peace be upon them all. 
NB: Legislations may change according to the circumstances, people nature, time nature, but the core creed never does.

As the final prophet now is Muhammad PBUH then Muslims are those who worship God alone associating no partners with him, and follow the legislations sent with Muhammad PBUH

So, whoever follows him (prophet Mohammed) is a Muslim and whoever doesn't follow him is not a Muslim, because this one will have not surrender to God Almighty, but surrendered to his whims.

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The One True God (Allah) called the believers Muslims (submitters), according to the Quran chapter 22:78
“… the faith of your father Ibrāhīm. He (Allah) named you as Muslims earlier …”

Allah tells us in the Quran that ALL his prophets were Muslims. Let’s take a look:

 __Prophet Abraham*
(131) When his Lord said to him, "Submit", he said "I have submitted [in Islam] to the Lord of the worlds."
( 132 ) And Abraham instructed his sons [to do the same] and [so did] Jacob, [saying], "O my sons, indeed Allah has chosen for you this religion, so do not die except while you are Muslims."
( 133 ) Or were you witnesses when death approached Jacob, when he said to his sons, "What will you worship after me?" They said, "We will worship your God and the God of your fathers, Abraham and Ishmael and Isaac - one God. And we are Muslims [in submission] to Him."
Qur'an (2:131-133)

“Ibrahim (Abraham) was neither a Jew nor a Christian, but he was a true Muslim (submitter).” Qur'an(3:67)

 __*Prophet Jesus and the disciples*
“The disciples  said,"  We   are  supporters  for Allah . We have  believed  in Allah and  testify   that  we  are  Muslims  [submitting  to  Him]." Qur'an(3:84)

__*Prophet Joseph*
“… Make me die a Muslim and make me join the righteous.”Qur'an(12:101)

__*Prophet Moses & the sons of Israel*
And Mūsā said, “My people, if you have believed in Allah, then, in Him place your trust if you are obedient.” Quran (10:84)

*The magicians of Moses*
“O our Lord, pour out patience upon us, and cause us to die as Muslims (those who submit to you.)” Quran(7:126)

__*Prophet Lot*
“but We did not find in it any Muslims, except one house.”Quran(51:36)

 __prophet Soulmun*
“…"We were brought the knowledge before her, and we were Muslims." (i.e., we surrendered "to Allah"). Quran(27:42)

And from that, the Islam that the Queen of Sheba proclaimed, when she declared surrender to her Lord, repented of her shirk(polytheism), asking forgiveness for her sin, as mentioned in Qur'an: 
." She said, "My Lord, indeed I have wronged myself, and I submit with Solomon to Allah, Lord of the worlds." Qur'an (7:44)

Christians and Jews are NOT Muslims, As for when Muhammad, may God’s peace and blessings be upon him, was sent, they disbelieved him, and they were not Muslims, and for this reason it is not permissible for anyone to believe that the religion of the Jews and Christians to which they owe today is a true religion acceptable to God equal to the religion of Islam.

Allah said in Qur'an: 

"Indeed, the religion in the sight of Allah is Islam. And those who were given the Scripture did not differ except after knowledge had come to them - out of jealous animosity between themselves.And whoever disbelieves in the verses of Allah, then indeed, Allah is swift in [taking] account" Quran(3:19)

And He said “And whoever desires other than Islam as religion - never will it be accepted from him, and he, in the Hereafter, will be among the losers." Quran(3:85)

And this “Islam” that God referred to is “the submission to the One True God Allah, following the legislations He sent with His final prophet; Muhammad PBUH.

Allah said in Qur'an: 
"....."This day I have perfected for you your religion and completed My favor upon you and have approved for you Islam as religion" Qur'an (5:3)