I believe this is the story "Cobwebs" by Ray Brown, which was only published in the August 1987 issue of Analog.
The story is framed as a backgrounder for a new generation of non-telepathic children who are going to grow up to be the next generation of military leaders since they can't be fooled into overlooking the aliens.
The story then skips back to show how the (all telepathic) people only see what the group consensus is, so everyone appears (to one another) to be young, healthy and good looking. Their city is beautiful, and it isn't until a transit pod falls from its tube that someone (who actually goes and pokes at the tube along its path) realizes there are holes that nobody is noticing.
There is a kid who isn't telepathic, whose mother keeps in the house all the time. This kid sees aliens (who are hostile), and his mother (who has looked through his eyes) believes him, but everyone else thinks she's crazy. After all there hasn't been an alien spotted in town for years and years...
Once the problem with the transit tube is discovered, some of the leaders go visit the kid, and look through his eyes and are aghast at what they see. There's a disease or parasite that people catch - that they thought had gone away - that makes their nose and chin grow so they look like classical witches. The narrator reacts badly when he finds out his wife has it (which she immediately sees, because they're all telepathic), and then has to deal with the guilt of that reaction, especially when he realizes he probably gave it to her.
They see the town falling apart, everyone in much worse shape than they expected, and aliens walking freely through town. As soon as the aliens realize that they've been spotted they attack, and only the kid, who becomes their general, can really trust what he's seeing.
There's a realization somewhere along the way that there should have been many more non-telepathic children born over they years, and the aliens have probably been killing them.
