Noun and の adjective
うよく
自分は、極端な右翼思想を持って生まれたように感じます。
I feel that I was born with extreme right-wing ideas.
The right wing is the right wing. As in, "right wing politics" or "right wing beliefs."
This is a jukugo word that uses the on'yomi readings of the kanji. You haven't learned this reading for 右, so here's a mnemonic to help you:
Those in the right wing love eating uni (う), not because they like the taste, but because uni is expensive. Picture some right-wing people in your mind right now and watch as they try really hard to pretend they like eating uni as they shovel buckets of it down their throats.