I believe there many possible 'types of interaction' towards the gods, including indifference.

1: Indifference/inaction
2: Worship (i.e. recognize that they are superior and that we as mortals are inferior)
3: Following (i.e. trying to follow their path... it's more like a self-improvement thing compared to 'worship')
4: Do ut des (I give so that you will give): a relationship with the gods based on offerings towards them so that they will give favors to us humans in return. That's for example what the government did in Ancient Rome.
5: ??? no specific name: a relationship with the gods based on gratitude. The gods have already given us so much good stuff, so it's natural to display gratefulness towards them
6: Learn their teachings, and achieve new metaphysical knowledge.
7: Curse them, hate them.

Etc. etc.