For this I normally take it as a bit of a sloppy progression where it's the same chord being played... but it's a different sound of the chord... As quickfingers said the open strings are basically there to add to the fullness of the chord... and the absence of them is to get the very basic sound of the chord... to give the feel of chord movement in the song... I wouldn't mute any of the strings. A muted string will change the dynamic of the chord if you're plucking all the strings. I would simply strum the strings that it's telling you to strum. Normally if the tab calls for a muted string with the fret hand it will be noted as an X in the tablature. So practice selective strumming where you're only strumming the middle 3 or 4 strings...

I like to call this type of chord work "sloppy chord work" because usually it's not the exact same throughout the song... You might be able to add in the E string for more bass or add in the high e string to get a nice treble when you feel like you need it... or if you want to further change the dynamic of the song... Just try to work it out whichever way sounds best when compared to the original recording... But like I said... I would try to play it without muting the strings. But that's just me.