Literally: apprehension – fear – hate – get tired of
Alternately: To fear and hate something. “Feelings of dread and aversion.” Afraid to a degree that makes you want to find a way to escape the situation.
Notes: This yojijukugo simply joins two two-character compound words together: 畏怖 is to recoil from something in fear; 嫌厭 is to dislike something enough that it shows in your attitude (a relatively high bar in polite Japanese society). Hundreds of millions of people around the world are feeling it right now because millions of people in rural USA felt it in response to a black man daring to be president.