That requires a cite.
It’s true that churches are highly segregated, but it’s not true that it’s due to heavy racism. To be honest, no one is completely sure why it happens. The first thing to note about American Protestantism is that it essentially functions as anarcho-communism. There is nothing preventing people from choosing their own rough collective in which to belong. American Protestants as a general rule engage very loosely with their theologies and most either do not understand or don’t care about the differences between say a Baptist and a Methodist or an Episcopalian and a Lutheran. They are more likely to focus on modes of worship than actual theological differences. This isn’t necessarily a ‘hyuk-hyuk, what a bunch of dummies’ issue, but is rather rooted in American Protestant individuality where it is completely acceptable and even expected to have disagreements with your church. You will frequently see denominations that are relatively liberal in leadership whose congregants are one step away from snake handling. My own denomination is relatively liberal in most things, but you can go to little country churches that think all of the bishops are going to burn in hell. It’s extremely common to bounce between denominations and churches throughout your life. Barma Group is a Christian polling and data firm and has found that people are more likely to change their religion over political differences than their politics over religious differences. In other words, the default behavior is that if your pastor is saying something you don’t like, you simply leave. Pastors that confirm presuppositions are the popular ones BECAUSE they confirm presuppositions, not because they are changing people’s minds. Denomination shifting is very normal and people flit between denominations their whole lives.
OK, with that said, you start to see where integrated churches run into problems. Leaders and pastors can talk about integration all they want, but deep down, people don’t want it. The reasons why are complex. There have been interviews with people in integrated churches that have fallen apart and there’s not a good answer. There are themes though. The first is obviously simple grouping behavior. These integrated churches that have fallen apart tend to view the other racial body as ‘other’ and a competing interest. This is not uncommon among members of the same racial groups as well. It’s very common to hear complaints about ‘cliquey’ churches or to see divisions over education level or mode of worship (e.g. hymns vs stage shows.) Race is an easy line to default to.
When you have this grouping behavior, you start to have power struggles. People who are going to church for ostensibly spiritual reasons frequently have difficulty dealing with these power struggles. When they occur, the default behavior is to leave as soon as you see which way the wind is blowing.
There’s also an issue with cultural modes of worship. One of the big paradoxes of American Protestantism is that the most liberal and progressive denominations are also the least integrated and it’s not even close. Episcopalians are about as welcoming and progressive of a church as you’ll ever see (They frequently poll as the farthest left religious group in the country, including atheists and agnostics-though Jews sometimes beat them depending upon the issue and poll.) and they are also 90% white according to Pew. Mode of worship is one of the main sticking points. As I said earlier, American Protestants tend to identify much more strongly with mode of worship than actual theology (within limits of course) Evangelicalism and Fundamentalism as I mentioned above owe much of their mode of worship to black southern churches. Pastors screaming at the congregation, running back and forth across the stage, congregant hands raised in the air, fast paced music, congregational feedback, etc. are things that are very common in both black churches and white Evangelical churches. They are very uncommon in white mainline churches which frequently function more like a university lecture than an emotional experience. What we know is that mode of worship is extremely important to people. Changing those traditional modes of worship causes a great deal of dismay and is an extremely common source of church break-ups. When churches begin to integrate, one of the big sources of discord is mode of worship (It might be the largest single thing, but there are no studies, only anecdotes and it gets mentioned more than anything else.) People have these very strong preconceptions about what church ‘should’ be and become very uncomfortable when even minor changes are made to that. When white people begin coming to black churches in number, there is often a perceived fear that they will make the services ‘dry’ or ‘boring’ or ‘limit the Holy Spirit.’ Conversely, black people coming to white churches often bring up fears of ‘emotionalism’ or ‘services extending forever.’ Again, this is MOST pronounced in extremely liberal churches largely because there is such a divide between their modes of worship. When you begin to meddle with the traditional social scripts that people come to expect from churches, it causes serious problems. A good anecdote is Prince Harry and Megan Markle’s wedding. They had a black Episcopalian minister there named Michael Curry. Reverend Curry’s sermon ran less than 15 minutes and if you have ever been to a ‘black church’ was extremely formal and subdued (I recommend watching it if you haven’t, excellent sermon (https://www.youtube.com/watch?v=RdIZpos-ME4), but I digress.) For the traditional Episcopalian crowd, it was ‘long’ and ‘fiery.’ and you could see discomfort on the congregation’s faces at times. It was a noticeable intrusion on traditional norms that provoked comment. It would have been interesting to see how they would have reacted to most of the southern black ministers I have heard through my life. Pearls would have been clutched I’m sure.
To get back to the topic though, grouping behavior is common to humans and in environments that don’t require togetherness frequently sort. It’s not necessary to posit vehement racism as the source when simple mundane human behavior suffices. Of course, that doesn’t mean that we shouldn’t work to overcome these sorting behaviors, but it’s not necessary to demonize them either.