First of all, isn't it a bit dramatic to say "your entire being opposes" your task? It's not like you're out committing genocide or something. You're programming, and you have to work on a crappy programming task. Every programmer who ever worked a professional job has had to do this at some point. If the very fiber of your soul is wrapped up in your employer's MegaAccounting Client V3.0 REST API, I'd recommend re-thinking your emotional attachment to your job.
That money you get every two weeks is called "compensation" because it is compensating you for your time, which you would probably otherwise spend doing something more pleasant. This is the realistic world of grown-up work life.
If your company's Marketing bone-head says the customers want a green oval button instead of a system-standard button, well, it's stupid, but I'd laugh at how much they're paying to get this ridiculous code written and just write the damn code. It's really not worth losing sleep or sanity over. Not being emotionally attached to your work allows you to shrug off the stupid stuff that Really Doesn't Matter.