As Christians we are a called people. We are called to bless even our worst enemies. How much more should we pray a blessing on other in the body of Christ! Very much especially so for those with whom we disagree, or hold a different view from our own.
If we ask a blessing on them, it is up to God to decide what He can and cannot bless in what they are and what they are doing.
We are not asked to understand each other first. If there are some elements in the church who really aggravate us it may be more useful to pray a blessing on them to interact in a critical spirit. As we pray we being to realize just how much God cares about these who we, more often than not, do not give a second thought.
We can pray blessings on non-Christians - as well, and this is something any one who lays claim to following Christ would find themselves doing in the first place. It is a bit like making a homemade Christmas card. Where ever the glue has stuck to the paper the glitter will stick in the glue, the rest only roles off; and even a little of the glitter can be enough to spell out a loud and clear message.
May the blessings of our Lord Jesus Christ be with you and yours, always - even to the end of time.