[JonPR]

If I was playing that line, I'd probably fingerpick it (so no strings need muting).

But if I thought it sounded better strummed - I'd lay a spare fret hand finger (or two) across the 3rd and 4th strings. E.g, I'd fret the top strings with index and pinky, leaving middle and ring able to touch the other strings. Of course when strumming I'd aim the pick at just the top 2 strings anyway (not all 6!), but it's hard to avoid hitting at least the 3rd string, hence the fret muting.

I wouldn't palm mute, because it's awkward to only palm mute lower strings and leave the top 2 free to ring. However, the palm mute position does enable more precise picking of the top strings, avoiding the pick touching the neighbouring strings. But I still find I'd instinctively fret mute the 3rd string at least. The other advantage of the palm-on-bridge position is that that top strings can also be damped, to give a suitable "steel pan" effect.

BTW, the open D string should sound fine on the first bar, because it's the root of the chord. In the second bar (same top strings riff) the chord is G, so technically both 3rd and 4th strings could ring open and it ought to sound OK. But I can appreciate they can sound too loud in comparison with the lead line. (And when the riff moves up, the chord is A, so both 3rd and 4th strings will definitely sound wrong.)