Victorian Sky, it sounds like your congregation needed to be reminded of the following two scriptures...
*** Rbi8 Matthew 12:1-8 ***
At that season Jesus went through the grainfields on the sabbath. His disciples got hungry and started to pluck heads of grain and to eat. 2
At seeing this the Pharisees said to him: "Look! Your disciples are doing what it is not lawful to do on the sabbath." 3
He said to them: "Have YOU not read what David did when he and the men with him got hungry? 4
How he entered into the house of God and they ate the loaves of presentation, something that it was not lawful for him to eat, nor for those with him, but for the priests only? 5
Or, have YOU not read in the Law that on the sabbaths the priests in the temple treat the sabbath as not sacred and continue guiltless? 6
But I tell YOU that something greater than the temple is here. 7
However, if YOU had understood what this means, ‘I want mercy, and not sacrifice,’ YOU would not have condemned the guiltless ones. 8
For Lord of the sabbath is what the Son of man is."
*** Rbi8 Matthew 12:10-12 ***
So they asked him, "Is it lawful to cure on the sabbath?" that they might get an accusation against him. 11
He said to them: "Who will be the man among YOU that has one sheep and, if this falls into a pit on the sabbath, will not get hold of it and lift it out? 12
All considered, of how much more worth is a man than a sheep! So it is lawful to do a fine thing on the sabbath."
(That second one could also be applied to the blood issue)