FrDavid96:
That isn’t the time for the priest to give blessings.
The monsignor at my mom’s parish always invites people up for a blessing during communion if they aren’t in the position of receiving the Eucharist. It is a nice thing to do, especially considering many of the people don’t understand the full meaning of communion, but they do understand what a blessing is. It is a small gesture that I have actually seen have a big impact on some. I don’t think Jesus would turn away from blessing someone in that situation.
For non-Catholics, it is confusing to go to Mass at the same parish and for sometimes it to be “OK” and for other times it isn’t. It would be helpful if the congregation was given a head’s up on the protocol prior to going up and being turned away. Perhaps a laminated card in the pew, indicating the protocol for the parish?
I have seem some very embarrassed people going up with their arms crossed because that is what they were told to do previously, only to be sent on their way without a blessing. Not exactly a great way to encourage them to return for future Masses.