What is the basis that some Protestants teach the non-necessity of baptism for salvation?

In Acts 8, we have the story of the Ethiopian Eunuch and Philip. Philip explains Isaiah to the Eunuch, then the good news about Jesus.

And as they were going along the road they came to some water, and the eunuch said, “See, here is water! What prevents me from being baptized?”[b] 38 And he commanded the chariot to stop, and they both went down into the water, Philip and the eunuch, and he baptized him.

The feature that is emphasized is the Eunuch's humility, enthusiasm and obedient faith. I believe that viewing Baptism through the lens of a required ritual robs it of its intended purpose: freedom. Baptism is about freedom, not rituals and laws.

I once invited a friend to attend my church. After a month or so, and after hearing that she had prayed the sinner's prayer with the pastor, I prayed silently that she would desire to be baptized. I said nothing to her, not wanting it to be an added burden or regulation on top of her salvation. A few days later, she declared her desire to be baptized. That fall, the appointed day arrived, but she had to be hospitalized for a severe migraine, and could not be baptized. In her case, something did prevent her from being baptized on that day, unlike the Eunuch. A week later, her baptism was rescheduled. Upon entering the water, she later said, she felt something come out of her. It later turned out that at the moment of her baptism, she was delivered from what had been years of chronic migraines.

Baptism is not a requirement, a rule to be followed. It is a gift, and the already saved person eagerly runs to receive that gift and the freedom that accompanies it.

Credo-baptists (note: not all Protestants) that hold the views you refer to, rely more on very clear soteriological proof texts that are not as open to alternative interpretations* as the verses you have cited such as:

8 For it is by grace you have been saved, through faith—and this is not from yourselves, it is the gift of God— 9 not by works, so that no one can boast. 10 For we are God’s handiwork, created in Christ Jesus to do good works, which God prepared in advance for us to do.- Ephesians 2:8-10 NIV

Baptism is something we do - a work, albeit a good one. Verse 9 quoted above would therefore exclude it from being a prerequisite for salvation, verse 10 implies that it should be a consequence of salvation. So the normal pattern is for sinners to respond to the gospel and receive grace through faith to be regenerated inwardly, they would then witness this inward transformation to the world through the rite of baptism. However, if there are extenuating circumstances - eg, they hear the gospel and believe it, but die before they can receive baptism despite their intention to do so - then the normal pattern can indeed be varied:

• A relevant counter-example to the idea that baptism is necessary to salvation, is the thief on the cross (cf. Luke 23:39-43): Jesus' promise to him that he would be in paradise was despite the impossibility of him undergoing baptism. The dispensationalist argument that this example is not relevant because it occurred prior to the resurrection and the outpouring of the Spirit is specious - this man was the first believer to trust in the crucified Christ for salvation.

• Another case in point is Cornelius and the members of his household (cf. Acts 10:44-48) - clearly they received God's grace for salvation before they were baptized (in water) as it was only thought of once they were already manifesting the outpoured Holy Spirit.

Baptism is regarded by credo-baptists as an outward sign signifying an inward work - it is not the sign that has substance, but that which it signifies. An analogous question is "Is it necessary to have a wedding ceremony in order to be married?" Even though in the normal course of events, a wedding ceremony is preferable, it is not strictly necessary. Yes, it does remain a very useful sign of the something of greater substance that it is signifying; nevertheless, if circumstances demand, an elaborate wedding ceremony can be eschewed as long as the substantive elements of marrying are observed.

Note: even though Baptism may be regarded as not absolutely necessary for salvation itself, there are excellent reasons for getting baptized and a decision to delay or entirely forego the rite should not be undertaken lightly - in this sense, to characterize baptism as 'totally optional' is misleading and should be regarded as false doctrine (incidentally, you mischaracterize Paul if you think he is saying baptism is 'optional').

_{*All the verses you cite are ambiguous to some degree as there are at least six distinct types of baptism referred to in Scripture. Additionally, there is a 'washing with water through the word' referred to in Ephesians 5:26 that appears to be a distinct process to any of those kinds of baptism. The church fathers and Luther are more explicit, but Credo-baptists think they have erred on this point and have no hesitation in contradicting them when they are sure of their own ground.}

Let me state the views of those who believe baptism is not necessary for salvation. (It's not just Protestants by the way - Catholics teach that actual physical baptism is not absolutely necessary for salvation. There are several circumstances where substitutes for it are acceptable).

• "Born of water" might mean several things other than baptism. It might mean cleansing from sins, for example.
• The Acts and Matthew passages are indeed commanding baptism. But that doesn't mean that a failure to do so results in loss of salvation. We all fail to carry out the commands of Jesus at one time or another - that's what sin is, and Jesus forgives us for it.
• The washing of rebirth is not necessarily baptism. Rebirth cleanses us from sins, and in that sense is a washing. The rebirth may or may not happen at the same time as baptism
• Hermas says (in paraphrase) "the remission you received through baptism is the only one". But that doesn't mean baptism is the only way to receive it. I could say "The brand of juice you bought at the corner store is the only one with real oranges in", but that doesn't mean I can only buy it at the corner store.
• Luther, Origen, Hippolytus and Tertullian are not God, and are not infallible. What they write is their own opinions. If a Christian chooses to have a different opinion, that's entirely up to them.

It should be said that Christians who say that baptism is not absolutely necessary for salvation don't deny the importance of baptism, or that it is a command from God, or that everyone should be baptized. They would just say that God is capable of forgiving whoever he wants to forgive, and isn't restricted by any rules.