Is Christianity mainly about the Spirit catching people up into the progression of heaven on earth? Or is Christianity mainly about building institutions, societies, and laws that benefit the individual conscience and familial aims?

We see both in the Scriptures. Spirit and structure. 

As Christians, we engage in politics because of the Incarnation. Because Jesus is both God and man, heaven and earth are coming together. The earthly king is not God, but humans have the ability in partnership with God to bring His rule into ours. 

The messy part is how that happens and with what sort of methods. Many Christians disagree on these things, and we must guard our hearts against resentment.

May God bring us to repentance, extend His grace towards us, and show us how to love one another so that we can receive His vision for heaven on earth in all its nuance and beauty.