Does Cap have a reason for why he's against the registration act beyond looking out for his friend, who despite being under mind control, was still responsible for international terrorist acts? That would be pretty irresponsible of him.
How about Tony Stark. First movie he says fukk the government. Then he's responsible for tech that causes catastrophic damage worldwide. He rides off in his drop top screaming fukk all y'all nikkas in Swahili. Now he's siding with the government?
In the comics the govt was too heavy handed and i guess cap was reminded of the same shyt when they tried to shove the MRA down the xmen's throats and overall the killing of people who resisted wasnt a good look either.
I assume the military and govt turns on cap because of his unwillingness to yield to authority... even in cap 2 :
He knows people in positions of power will use the registration act for their own ends and he doesnt want that, so if that meant screaming fukk the police, cap is gonna be there, doing what's right... it's simple as that...