Do Moral Values change over time?

It is often claimed that moral values change greatly over time as societies “advance”. For instance, it is often claimed that modern societies are morally superior for not killing witches or shunning homosexuals. But perhaps what this apparent progress actually shows is that while we are scientifically superior, we may actually be morally similar, to ancient societies. Surprisingly similar moral values often underlie very different historical manifestations of morality. How can this be so? It seems to me that when we combine traditional moral values with increasing scientific knowledge, we actually get changes in cultural practices that are more just and compassionate. Let me unpack this with some thought experiments:

What counts as "Christian"?

Recently I was in an online discussion about whether a group of people and the ideas they represent are "Christian". My initial response was that if they have been baptized into Christ, and they do not renounce that baptism, then they are Christians. They may be faithless Christians, bad Christians, hypocritical Christians, uninformed Christians, unjust Christians, but they are still Christians.