Ok so Danse wants me to join the BoS to do another mission. Will saying yes and doing the mission have any effect on other factions in the game?

Not right away, but there comes a time when faction choices has to be made. Also it will grant some negative reputation with Preston Garvey. The companions have their own agendas and preferences, so watch out.

An in game prompt will tell you if an action will effect your relations with another faction, so don't worry.

Thanks.