This word is acceptable for play in the US & UK dictionaries that are being used in the following games:

• Lexulous
• Wordscraper
• Wordosaur

v. Present participle of desensitize.

adj. making less susceptible or sensitive to either physical or emotional stimuli. Opposite of sensitizing.

adj. making less susceptible or sensitive to either physical or emotional stimuli

"Americans may succeed in desensitizing themselves to what is going on, as many did with slavery, but most Americans feel decidedly uncomfortable about the stilled heartbeats and brains of 1.5 million human fetuses every year."

numbing   

desensitize