The changing tarot cards definitely have some meaning.

As I've begun to romance Sera her card has changed significantly. Also, following a very personal quest involving Dorian, his picture changed as well.

I believe that each character has at least three cards, one default, one that indicates a deepening friendship, and another that suggests disapproval/increased hostility. 

For me, so far only Sera, Dorian, and Blackwall have changed from their default, all three because I spent time improving my relationships with them and doing at least one personal quest/favor for each. I try to keep everyone happy by speaking to them individually and telling them what they want to hear, but major plot decisions inevitably sway some followers in one direction or another. So far cole is the most disapproving, I think because his omniscient nature causes his opinion to change even when he is not in my party.