[Campion]

The simple answer, on what authority, is other scripture. When the whole of scripture is studied, and the difficult passages worked out against each other, basing interpretation of the foundation that the Bible is inerrant, these issues work out rather nicely.

Then why do some Protestants, basing their belief on the Bible alone, accept infant baptism, and other Protestants, basing their belief on the Bible alone, reject it?

[FactQuest]

Then why do some Protestants, basing their belief on the Bible alone, accept infant baptism, and other Protestants, basing their belief on the Bible alone, reject it?

Obviously, at least one of them is wrong. I lean toward not baptizing infants. But, I'm willing to concede that I may be wrong about that. Underlying this whole difference is an underlying faith that baptism is not what effects salvation, and on that almost all Protestants agree. I would aruge that the Protestants that baptize infants do so more out of a tradition that is rooted in their Roman past, combined with, as you noted, no verses that prohibit it.