O'Brien told the Scotsman.com Saturday that some high-ranking Catholic clergy fear immigrant groups could "take over" in western European countries by having more children than native Christians.
The Scottish government encourages immigration to Scotland, but conservatives have claimed the flow of migrants could threaten traditional British values, the Scotsman said.
O'Brien said a guide who showed him around the Austrian capital expressed similar fears for Vienna. "She said: 'You know, we are losing our Christian Catholic community. We are not having babies, but the immigrants, they love babies, love families, love family life, have many many children, and soon they will be taking over,'" he said. "Basically, that reflects the views of some of our own church leaders at this time."
O'Brien did not mention any particular religion, but other Catholic leaders have publicly expressed worries that the rising Muslim immigration to Europe could tip the demographic balance.
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