That's not really surprising. I would probably laugh or at the least be entertained if some random stranger died in front of me, but would probably go berserk if it is someone I actually care about, as rare as they are. I believe Eren is pretty righteous, wanting to save the other squads who he does not even know.

Mikasa does not blindly support Eren. She blindly wants to protect him, so if Eren chooses a risky path, she would oppose it as much as she can. Only if that does not work, like when Eren obsessively wanted to join the scouts, will she reluctantly join him. Funny thing is, Eren listens to everyone else's opinion excluding Mikasa's, when it is clear whose opinion will actually keep him safe.