By asking for synthetic...are you talking about the soles or the upper? For a good pair of dance shoes the soles should be suede or chrome leather, but the upper can be made of anything. There are several options, one of the popular ones right now is an upper made of lycra, you can also find canvas.
Supadance 800-888-5429, International 800-745-4758, Werner Kern 800-354-3101, Freed 800-433-5541, Dance Naturals 619-756-4819, Elegance 818-788-3216...these are just a few manufacturers that can send you a brochure of all styles and options!
Happy shoe hunting!
Larinda