Keep in mind several of Jesus's followers were senior members of the religious leaders of His day. So, I am not sure that statement is true.
Meanwhile, several of my church's regular attendees are homeless people and they are welcome, so which people don't you think would be welcome. Perhaps you attend the wrong church or have a misunderstanding of what many churches do.
One of my affiliated churches, opens up all its bathroom and shower facilities to the homeless on Monday through Saturday mornings to use and feeds them breakfast.
Many churches continue to welcome anyone who comes.
As a young man, my friend (an ex-Satanist converted Christian) and I led a Bible study for Satanists and Witches (Wiccan) interested in God's word. I would call that pretty inclusive.
That said, I do understand parents who are nervous about any strangers around their children and so while our church services are open to anyone, the Sunday school area is pretty restricted.