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Don't misunderstand me. If Tony Blair has experienced a true conversion, and wishes to embrace the Catholic Faith, then I would be delighted for him. I experienced a major conversion and returned to the fold nearly fifteen years ago, and it is something I shall be eternally grateful for (literally!) I wouldn't dream of placing obstacles in the way of anyone else.
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Conversion also means renouncing the mistakes of the past, and admitting that they were wrong. This change of heart can be very difficult for one's relationships with friends who shared previous ideas and ideologies, and sometimes there has to be a parting of the ways. This isn't easy, but for most people it is a quiet and private affair.
However, Tony Blair is a public figure. He may protest that his faith is a private matter, but Church teaching doesn't just cover private belief; public behaviour is also involved. The penances given in Confession were once public, and penitents had to stand at the door of the church in sackcloth and ashes for a certain period (determined by the sin) to prove their contrition (this is where the idea of "days off" with regard to partial indulgences arose... ) Mr Blair's voting record on abortion is public knowledge (he has, for example, voted three times to allow abortion up to birth) as is his stance on homosexuality (he said that he "did a little skip" of joy when the first Civil Partnerships were celebrated.)
So, If Tony Blair wants to be received into the Catholic Church, then, in order to avoid causing scandal (which is still a sin, though it isn't fashionable to mention it in these days of public soul-searching on Trisha and Oprah) he really must speak out and renounce his former actions in public. He will need to stand up and swear to accepting the whole of the Catholic Faith. In public.
I also read that Mr Blair wants to be considered for the diaconate. This strikes me as trying to run before you can walk. The report also added that he thought that he could be fast-tracked due to his previous role as Prime Minister. If this is true (and I put emphasis on the "if"), then it is one of the clearest indications that he is definitely not suitable for ordination.
You can read a report on Tony Blair's impending visit in the Daily Mail (which cites Blair's stance on abortion as an impediment.)
UPDATE: Although no earth-shattering announcements have been made, Fr. Ray posts a picture of the meeting between the Holy Father and Tony Blair (and I love the caption), and Fr. Tim has obtained some amazing photos of the lunch given by Cardinal Murphy-O'Connor at the English College. Oh, and the blip in the Earth's gravitational field is the result of several of the English Martyrs rotating in their graves...