re: How is it possible that some Protestant churches support gay marriage?

That is why I said "mainline Protestant" churches.

For those that don't know - those are some of the the older Protestant churches of the U.S. - the most politically influential churches most of U.S. history, but have experienced a pretty dramatic decline in the last 60 years or so.
They include - the Disciples of Christ, the Episcopal Church, United Church of Christ, Presbyterian Church USA, United Methodist Church, and the Unitarian/Universalist Church. I am probably leaving out a few.
Apart from some non-denomination churches - these are most likely the churches that will fly the Pride flag, have a black lives matter sign, and a lesbian pastor. They are also full of white senior citizens.

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But Augustine himself did not believe in sola scriptura or sola fide.

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I disagree, at least in terms of affirming the principle of sola scriptura, and I also disagree that Augustine didn't have some understanding of salvation by grace alone. It's why the doctrines of grace of Calvinism are often times called "Augustinian", especially in terms of contrasting total depravity with free will. The Reformers referenced Augustine heavily for their "Calvinistic" soteriology.

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And the New Testament was written in the first century but not finalized until the 4th century.

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That which is Scripture was completed at the end of the 1st century. Those letters--once written--were circulated throughout the Church immediately where copies were made. While not everyone had every NT book/letter at all times, that is irrelevant to what sola scriptura actually teaches, which is that the only infallible rule for faith and life of the Church was found in the writings that are God-breathed and preserved for the Church. The oral traditions of the Apostles were not preserved, which is why I said that there is no document in existence that lists out every oral tradition of the Apostles given to the Church.

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Martin Luther, John Calvin, and John Darby and John Wesley did not know the early church fathers or the apostles.

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They didn't need to know them personally. They had their writings to reference and quote from.

BTW, I'm a fan of Luther and Calvin, but I'm not as much of a fan of Darby and Wesley.

Any protestant church believe or support whatever their narrative

You are talking about the Methodist of whom are having a very ruff spilt right now. The episcopal church is gay friendly.

Presbyterians would just assume burn the ones mentioned above as heretics.

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How is it possible that some Protestant churches support gay marriage?

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Protestants are not tied to a singular central authority based on scripture.

So you have some that are very strict adherence to core Christian values and govern themselves very well. Then others that stray so far from it that you could barely recognize it as a Christian church. That's the landscape right now and has been for a while.

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Not as common bread nor common drink do we receive these…The food which has been made into the Eucharist by Eucharist prayer set down by him, and by the change of which our blood and flesh is nurtured, is both the flesh and the blood of that incarnated Jesus-St Justin Martyr.

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“the bread which our Christ gave us to offer in remembrance of the Body which He assumed for the sake of those who believe in Him, for whom He also suffered, and also to the cup which He taught us to offer in the Eucharist, in commemoration of His blood"(Justin Martyr, Dialogue with Trypho, 70).

Again, even the ECFs weren't clear on exactly what they meant in what they said at all times. When the RCC or Orthodox say that the ECFs taught transubstantiation and the real physical presence, they are forcing current beliefs into history.

Most of the quotes from the ECFs regarding Jesus' body and blood can be quoted by us in the Reformed tradition that see the elements so closely tied to the reality of Christ that we can call them His body and blood, even though we don't believe they are transformed into His physical body and blood.

Ok. Well, I feel like you are kind of reaching to make your quotes mean what you want them to. “Not as common bread or common wine”, “and by the change.” These quotes seem to be undeniable.

But whatever. I know at the end of the day we won’t agree. Ultimately, I hope we all achieve salvation.

Can you describe your view of faith alone? How do we achieve salvation in your view?

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Protestants are not tied to a singular central authority based on scripture.

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The Bible and scripture is that authority. Granted, there typically isn't a gargantuan hierarchy and bureaucracy enforcing that authority, but that isn't necessarily a bad thing. The real churches hold themselves to the authority of the Bible and scripture.

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The real churches hold themselves to the authority of the Bible and scripture.

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Those very much do still exist. But they are fewer and farther between in the junk drawer that has become of the wide variety of protestant churches out there.