I can share what my baptism meant for me, but that won't answer your question totally as I probably have a slightly different understanding from Catholics or more traditional 'religions'.
For me, being baptised was an act of obedience as Jesus told us to be baptised. For me, baptism is (and was) a public declaration of the decision that I have made to follow Jesus and accept his sacrifice for my sins.
Personally, for me, it wouldn't have mattered which denomination I was baptised under, it's not being baptised into a religion, rather publicly declaring my relationship with Jesus.
At my church, we wouldn't encourage anyone to get baptised out of a sense of religious tradition or just because it's the right thing to do. As much as we can't judge the hearts of people, we would encourage them to understand what it means. It's declaring that you want to follow Jesus as your Lord and Saviour. (We also don't do infant baptisms)
Sorry if this sounded a little too preachy. I just couldn't leave that comment there. I understand the decision I made when I was baptised and I stand by that decision to this day.
So some people do