Even if Paul's and Manson's interpretations were the same, that black people had to fight for their freedom, the main difference would be how to do it. Manson's reaction was murdering the white establishment, and I'm sure Paul would never suggest that way.
But I tend to agree with zipp. Although "Blackbird" had already been related to civil rights in the past, not only by Manson, apparently Paul brought this interpretation too many years after. Actually I think it's valid for him to adopt the interpretation he wants, even if he didn't mean that when he wrote the song (but in that case he should clarify this).
In fact I do the same, I don't care too much about writer's original interpretations of songs, I just take the message that means something to my life. Words are words, they don't change, but the meaning always depends on the listener, especially when the lyrics are vague, as it usually happens in songs.