I think the article overreaches considerably. Speaking as someone who was a a very active young conservative in the mid-eighties as well as an avid Smiths fan, I'd have to say that much as I would have loved to regard the Smiths as my own kind politically, it never occurred to me to do so. Even to someone with every incentive to see them that way, they clearly were not a conservative band, not even indirectly, unintentionally or in terms of broad orientation. I distinctly remember some people being surprised that a conservative would like the Smiths.
That being said, they did not seem to me a band with a very distinct political character in the other direction either. The whole issue of their politics always seemed to me rather irrelevant to what they were about.
In that sense though, the article makes a valid point. There isn't actually that much in the Smiths that represents an obstacle for someone experiencing the world from a right wing political viewpoint. It's not like Matt Johnson or Paul Weller, where you just have to accept you're dealing with a different world-view. Where's the politics in Morrissey's lyrics? "England is mine, it owes me a living"? "The Queen is Dead"? Republicanism isn't or wasn't actually a particularly burning political issue. Vegetarianism? That's not a left/right thing.