I am currently inquiring into Orthodoxy, but I have been Catholic all my life, so I think I have a place in this discussion.
While I commend your efforts to encourage objectivity, this pope has made it so that transgenders can be baptized without repenting (that means a man receiving the sacrament with lipstick, a dress and a wig on), and he has many times done various things to support homosexuality in the church, such as protecting priests who commit sodomy from receiving the appropriate consequences. I don't think people should be expected to read a big official document before feeling a bit skeptical of his decisions on matters related to LGTV nonsense.
I really don't see how blessing two sodomites could ever possibly not be the same thing as endorsing their "union". We can ask a priest to bless pretty much anything, because blessings are always good. A tradesman can ask a priest to bless his tools. I can ask a priest to bless my garden. I can even ask a priest to bless a weapon, as long as the priest is not personally opposed to doing so, because this way I would be asking God to ensure that the weapon is not used in anger or for evil. But can I ask a priest to bless a dildo or a line of cocaine? How about abortion pills? I am no theologian, but I think not. You cannot bless things that are inherently sinful and satanic. That's just ridiculous on its face.