The number of Sanctuary points received when caring for a creature depends on a number of factors:

• The rarity of the creature (higher rarity → more points!)
• The level of the creature (higher level → more points!)
• Stat Boosts on the creature also count, to a lesser extent

You can always preview the number of Sanctuary points you will receive by pressing and holding the care buttons. Experiment with different creatures to see which give the most sanctuary points!

A good strategy to level up your Sanctuary faster would be to use rarer and high-level creatures!