Oh boy!
I hope your sister realizes that many non-denominational churches believe that infant baptism is bad, and I would even say wrong. They believe in “believer’s baptisms” where a child has to be of an age where they understand what it means to have faith, and can express it them selves. They don’t believe in confirmation.
I started out as a non-denominational Christian because I was sick of the labels with Christianity and just wanted to be “Christian.” Unfortunately (of fortunately) I learned that “Christian isn’t just Christian.” There are various dogmatic differences between many churches, and these culminate to huge differences in beliefs.
Does your sister know that non-denominational churches don’t believe in observing or celebrating anything other than Easter and Christmas? Anything other than that are considered “traditions of man,” and are otherwise bad. Tradition isn’t practiced, nor is it respected because it’s “man-made.” I once talked to a friend who was non-denominational about Lent and Ash Wednesday, and she had no idea about either one of those days. There is no Lent, Advent, Feast Days, etc.
What does all of that mean? It means that faith-life is not observed and celebrated in the same way. As Catholics for instance, Advent and Lent are meant to be spiritual journeys, filled with reflection, conscious awareness of the days coming up (Christmas and Easter), and during the process we may practice other traditions. During Lent, we abstain from eating meat because it’s a symbolic representation, and faith practice of sacrifice. Many non-denominational Christians would say “where in the Bible does it say that?” and then point out that it’s a “man-made” practice.
Non-denominational churches also come up with their own rules and beliefs. I could easily do a comparison between the belief systems just by looking at a few non-denominational churches in my area. Some churches will tell you that it’s A-Okay to have an abortion because it’s a “decision between you, your doctor, and God,” and some churches will say no. Some churches will emphasize the submission aspect of a wife while exalting a husband to a god-like status, and some churches outright dismiss submission/headship and instead say “it’s all equal.” I personally think the Catholic Church takes a moderate and reasonable view on that teaching.
Many non-denominational churches are actually part of the “Restoration Movement” of churches, where they believe they are going back to the “original” church practices and teachings of early 1-4th century churches. In other words, it means low liturgy or none at all, very loose structure of church services, and oftentimes Elders of the church authorities are the ones who make the decisions of what the church believes. There is usually overlap between non-denominational churches, Pentecostal, Assemblies of God, Church of Christ, and Baptist churches, but non-denominational does not ascribe to any label because they simply wish to be “Christian.” But they still have the label of non-denominational.
I would really urge your sister to have her husband take a look at the church’s website, take a look at the beliefs, mission, etc. and compare that to what Catholics are called to believe. There is a huge enough gap to fill in the pond between the UK and the US! Not to mention-- and I’ve heard of this happening before, and talked to people who’ve done this-- if your sister and her family decide to stay with that church after her son is baptized, when he gets older the church may push them to get “re-baptized” because infant baptisms are invalid baptisms according to many of these churches. I know a lady who was raised Catholic, became Baptist, and got herself and her entire family re-baptized because she doesn’t believe that the Catholic Church is a Christian church.