Albert Barnes on Matthew 12:4-5

House of God. That was, the tabernacle; the temple not being then built.

In the law. In the law of Moses.

Profane the sabbath. He referred them to the conduct of the priests also. On the sabbath days they were engaged, as well as on other days, in killing beasts for sacrifice, Nu 28:9,10. Two lambs were killed on the sabbath, in addition to the daily sacrifice. The priests must be engaged in slaying them, and making fires to burn them in sacrifice; whereas to kindle a fire was expressly forbidden the Jews on the sabbath, (Ex 35:3) they were obliged to skin them, prepare them for sacrifice, and burn them, They did that which, for other persons to do, would have been profaning the sabbath. Yet they were blameless. They did what was necessary and commanded. This was done in the very temple, too, the place of holiness, where the law should be most strictly observed.

(m) "shewbread" Ex 25:30 (n) "only for priests" Ex 29:32,33