From what I've learned, Sokrates was sentenced to death for corrupting the youth by defying gods and introducing strange ones. Yet, Protagoras of Abdera openly claimed: "Concerning the gods, I have no means of knowing whether they exist or not, nor of what sort they may be, because of the obscurity of the subject and the brevity of human life".
So why did Sokrates receive such a bad treatment as opposed to Protagoras, Diogenes, and other agnostic philosophers?
Four points:
Sokrates, as you point out, was prosecuted for 'introducing new gods' -- defying gods wasn't part of the charge. Protagoras isn't reported to have introduced new gods; he gets painted as a relativist, not as a founder of a new religion.
The testimony we have about Protagoras' view of the gods isn't straightforward. Late testimony paints him as agnostic/atheist, but earlier testimony -- Plato -- paints him as attaching great importance to piety.
There is a late story that Protagoras was charged with the same crime as Sokrates, but that he chose not to face the charge but leave Athens. The story probably isn't true, but still, the same idea did occur to people in antiquity -- just not early on.
The time and place where people could be charged with this crime is pretty narrow: from 432 BCE to about the 390s BCE, in Athens. Sokrates and Protagoras fit those parameters, but someone like Diogenes doesn't.
One late piece of testimony specifically which is key to the idea that Protagoras was atheist/agnostic, Diogenes of Oonoanda fr. 11 Chilton = Diels-Kranz 80 A 23 (tr. Waterfield):
Protagoras of Abdera held a view that was identical in meaning to that of Diagoras, but he did not express himself in identical words, in order to avoid the excessive recklessness of the view. So he said that he did not know whether there were gods -- but this is the same as saying that he knew there were no gods.
Diagoras, like Sokrates, was charged with asebeia and introducing new gods. But we know of only a handful of people who were: the only other known accusations are against Anaxagoras and Aspasia. Anaxagoras and Diagoras left Athens rather than face the charages; Aspasia was acquitted.
The only direct statement we have attributed to Protagoras on the subject is (Diogenes Laertius 9.51 = D-K 80 A 1):
Where the gods are concerned, I am not in a position to ascertain that they exist, or that they do not exist.
This is much milder than the kind of stuff we find characterised in the 400s as philosophers introducing new gods. The stereotype, captured in Aristophanes' plays and corroborated in a number of non-comedic sources, is that philosophers were personifying natural forces and treating them as new divinities: Aristophanes' Clouds caricatures Sokrates as treating Clouds, Breath, and Mist as deities; the Frogs has Euripides praying to Aither, Tongue, and Nostrils. This is a parody of actual religious teachers reinterpreting standard divinites as personifications: such as how the Derveni author interprets Zeus as 'Mist', and Kronos as 'Time' and 'Collision'. This is the kind of thing that seems to be understood as 'introducing new gods'. The statement we have attributed to Protagoras isn't like that.
Plato, who is much closer in time to Protagoras than any of our other sources, casts him as putting a high value on piety. Protagoras 323e-324a (tr. Lamb):
[Where good things are lacking,] only their opposite evils are found ... One of them is injustice, and impiety [asebeia], and in short all that is opposed to civic virtue; ...
and 324e:
Now consider: is there, or is there not, some one thing whereof all the citizens must needs partake, if there is to be a city? ... For if there is such a thing, and that one thing, instead of being the joiner's or smith's or potter's art, is rather justice and temperance and holiness [to hosion] -- in short, what I may put together and call a man's virtue ...
So there's a need to take a nuanced approach to philosophers' attitudes to the gods. It isn't a binary situation where either you believe in the standard gods without question, or you get executed. 'Introducing new gods' was a fairly specific charge, and it apparently didn't apply in Protagoras' case. Even in cases where a charge of asebeia was brought, it seems it must have been often politically motivated. The charge against Aspasia must surely have been for political reasons. In Sokrates' case we can't know if the charge was true -- if it was, Plato is hardly the one to tell us -- but there were certainly ulterior political motives there too, because of his involvement with Kritias, Charmides, and the murderous regime of the Thirty Tyrants.