I've been to a LOT of funerals.
At the crem, due to the fact there is one funeral after another, friends gather outside, and family arrive with the coffin. When the chapel is empty from the previous funeral, the undertaker indicates it is time and the coffin is taken in, followed by immediate family then the friends follow in after that.
Where there is a separate Church service, friends (+ colleagues, neighbours etc) tend to go into the Church leaving the front couple of rows for family. Family then arrive with the coffin and follow the coffin in to Church.
So, in neither scenario do the family arrive early and 'welcome people' IME.
I mean, where they are able, it is common practice to try to speak to people afterwards and thank people for coming, but it DEFINITELY isn't the place of anyone to go and tell them off, or criticise them in any way 
What is the matter with you ?