I've been in a LOT of Protestant churches, and seen a lot of variation.
Even when you say "Baptist" ... there are so many kinds, they can have very different ways of approaching it.
I've seen churches that baptize only to "correct" a deficient baptism (infant baptism or sprinkling).
Ones that require baptism as a show of membership to a particular congregation.
Ones that allow baptism for "rededication" at the desire of the one being baptized.
Ones that will re-baptise either Trinitarian or Jesus-name because the other was done.
I've seen churches that bring in a celebrated pastor or evangelist and he will baptize everyone who wants to be baptized (whether they have been or not - and generally everyone has been) - just so they can be baptized by that person, or participate in a "baptism-party" with many others getting baptized.
I once attended an outstanding play for Pentecost at a UPC church, and people were baptized as part of the play. Then after the play, lots of audience members came up to "be baptized" - LOTS of water splashing around everywhere, and the one doing the baptizing was a layman.
Many churches are very careful and don't treat it casually. Others will offer baptisms at the drop of a hat (the ones I have seen do this the most are Pentecostal and non-denominationals) - and some people can easily be baptized 10 times.
I've been baptized more than once, but I'm not sure if any were Trinitarian by a member of the clergy or not ... I need to speak with Father about it soon and see what they want to do.
But Protestants are ALL OVER the place with how they approach it.