Should universities be able to deny academically qualified applicants due to content on their social media?

Examples:

Should a Christian college be able to deny someone due to them posting atheists ideology on their social media accounts?

Should a Ivy League college be able to deny someone due to them posting nude pictures of themselves on their social media accounts?

Should a HBCU be able to deny someone due to them posting pictures of a confederate flag and far right winged ideology?

If yes, why?

If no, why not?