I think Green would do fine against Bird and Barnes wouldn't be terrible either. Heck Iggy did a great job on James, who is faster and stronger than Bird ever was (and isn't much shorter).
Iguodala guarded James well, because LeBron couldn't shoot at all that series. In fact, LeBron had his worst shooting season in a while all of last season. And his jump shot has continued to disappear this year as he slowly declines. I think a more apt comparison is how Igoudala deals with Durant. And he can't stop Durant at all.
LeBron could never really shoot, hate to break it to you (only a career 74% from the line). He went from a mediocre shooter to pretty solid in the past few years, but he's still very streaky.
Some games he won't miss, but it's not consistent.
He's not the best player in the world because he can shoot. He takes over and dominates due to his driving ability. A bad shooting night isn't going to hurt his game a whole lot (do you watch him much?) or at least not any where near as much as Andre Iguodala is gonna hurt his game.
Also, for the record, last season which you consider LeBron's worst shooting in a while, has him at .354 from 3 with 1.7 made per 36, compared to .340 and 1.3 for his career. Actually, it's his 4th best season shooting the 3, though i'm not sure about his percentages from 16-23 ft.
Iguodala allows GSW to do something that no other team in the league can do, aside from maybe SA, and that is defend LeBron largely 1 on 1. They don't care if LeBron gets his (which he did in that series scoring 40+ in 3 out of 6 games and averaging 36ppg) as long as the team's offense as a whole is locked down.
Glad at least the NBA noticed this and gave him the MVP trophy he deserved. Warriors probably still win if you replace Curry with a Lilliard-type, but they don't win if you replace Iggy with a Jeff Green or something like that. Fans will continue to not give him enough respect, but that's nothing new because he's been underrated for most of his career.