From Stand To Reason blog:
Yesterday on the radio show, Greg talked about the reasons he thinks that Jesus was referring to His followers. The people who are “blessed” are His disciples. The audience He’s addressing is a large group of those who have been following Him. And the last Beatitude, the specific announcement of blessing, is about those who receive persecution for His sake. And is immediately followed by statements that seem like an expansion on that idea with no textual indication of a break in his theme or audience.
Only Jesus’ followers would be persecuted on His account, and the encouragement about salt and light seem to be a exhortation to continue being His witnesses despite the persecution and difficulty. We often treat this passage as though there’s a break between verses 12 and 13, as though there’s a change of thought or theme, but there’s no textual reason to do so. It’s just that our Bibles are usually organization with the list of blessings stacked together and then a subtitle before verse 13. Read them altogether and see if it doesn’t seem to make sense.
If this entire text is addressed to Jesus’ followers, then that means that these are not general encouragements and can’t be applied to those apart from Jesus. These are specific blessings for His own.