The Church has no law about how a priest should handle latecomers in his parish. It is true that many priests get frustrated to see many of their parishioners’ laxity and nonchalance about coming to mass on time. The truth is, shutting the door entirely is rather too harsh a way to punish people. This is because there may be one or two people who are late for legitimate reasons. Also, it won’t be good to hinder parishioners from fulfilling their Sunday obligations (which BTW precludes arriving early at Mass). Maybe a more humane path would be better in resolving this problem. If such a priest insists on doing this after having been advised by parishioners, he could be reported to higher authorities in order that he may stop doing this.
When are you late for mass?
When you arrive later than the procession. Have this in mind so that you may participate more fully. The mass begins with the procession not the Sign of the Cross.