If I only had a book filled characters that looked like me, it would be a very sad, small world... too small and sad for any decent story to live in, in fact. It wouldn't simply lack POC, it would lack people of other nations, religions, genders, politics, sexual orientations, eras, educational levels... it would even lack people older than me, since at this point in my life, I don't know what that's like, either. It would be populated solely by Straight Male Norwegian-American Lutheran Suburbanite Engineers fifty-six years of age or less.
That's not a book you want to read. Trust me on this.
So, I just try very hard to avoid cliché and stereotype, learn what I can hope to learn about the differences, and do the best I can to not ignorantly produce the literary equivalent of blackface.
(Quick edit to note, I meant to respond to the original poster, but I think this works as concurrence with A.M. Bradley's words on the subject, so I'll leave it here.)
...
Regards,
Eric Fretheim
"It is perfectly okay to write garbage-- as long as you edit brilliantly." ~C.J. Cherryh
"Success is the ability to go from failure to failure without losing your enthusiasm." ~Winston Churchill