I'm reading the opinion now, and I would not have guessed that those particular justices would have made the ruling they did. Does anybody have insight into how this decision fits with the ideological views of the justices?
The conservative Justices generally favor looking at the plain text of the statute, while the liberal Justices are more willing to look at the broader implications and view a situation in functional terms. So it's unsurprising that the liberal justices, and Chief Justice Roberts who is less textualist than the other conservatives, were willing to look past the technicality Aereo was relying on to see that it was functionally equivalent to any other television streaming service.
Did it? The majority opinion was joined by 2 of the 5 conservative justices and all of the liberal justices. Three conservative justices dissented based on their reading of the law, which didn't seem particularly ideological.
