I've encountered a lot of this - still feeding dd once a day at nearly 2 years. I never got any negative comments in the early months, but once my dd was over 6 months it started, and often from women who had breastfed themselves! So you're not alone and at least you appreciate it's not entirely rational.
I think you're repulsed because it's still pretty unusual in our culture to breastfeed that long, plus when it does happen you don't tend to see it. After about 14 months my dd just had two breastfeeds a day, so they were both at home, out of sight. I think the only way to change people's feelings about extended feeding is for it to become more commonplace, and just a normal activity.
Maybe if you yourself continued after a year you'd find your attitude changing. I once got a shock when I caught sight of myself in a mirror with this toddler on my lap feeding! I'd somehow still pictured her as a baby. But the extended feeding happened so gradually that it just feels very natural to me, even now my dd can ask for it.
I'm in the early weeks of pregnancy, so am thinking I'll wind down the one remaining feed in the next couple of months, but I'm really happy that our cosy feeding relationship continued this long.