Fifth Head of Cerberus is a good starting place for reading Gene Wolfe.
The Book of the Long Sun is a great work, even if it does drag at times - and its main character Silk is one of the best characters of fiction of all time - this only really dawns on you as you're nearing the end of the tetralogy - it's an accumulative effect. The WHOLE 'Solar Cycle' (New, Long, and Short Suns) are the real masterpiece, not just the famous Book of the New Sun.
Wolfe's prose in all its forms (from baroque, dense, unreliable first-person to economic, crisp third-person) is some of the very best you'll ever read in fiction. Not every moment in every book is great (and a few of his books are skip-able), but there are almost always a number of elements in each book that make them totally worth it. Also, Gene Wolfe's whole body of art is something that builds up in the reader over a number of years of persistent reading. I know so many people think that's not worth it - but with Wolfe it really is. It's pretty awe-inspiring when you realise it's happening to you.
The more recent Wizard Knight duology is also great, contra some opinions. And I would guess just about any collection of his short fiction will thrill you and draw you on to more.
As to his politics, come on. Politics are politics. Authors run the gamut with them. His 'conservatism' (he says he's a Libertarian and there is a difference) doesn't seem to put off folks like Neil Gaiman and China Mieville and Patrick O'Leary, who are cutting edge fantasy artists who love Wolfe's artistry and therefore respect his worldview, even if they passionately disagree with aspects of it. He's not some neo-Nazi fascist after all. His stories show a huge sympathy toward all sorts of people from all sorts of backgrounds. That's one of the key elements of his body of art and a very attractive one.
'All we are saying... is give Wolfe a chance.