In Islam we use the right hand for the good things and the left one for cleaning and so on. All humans all over the world use the right hand to shake regardless of being Muslim or not. Now... a non Muslim [who doesn't know any better] will use his right hand to clean but suppose he doesn't wash it properly (by mistake). He then shakes your hand! Eek! All the dirt is transferred to your hand! But a Muslim uses a different hand for cleaning and will shake with the right hand so will never contaminate your hand. So a non Muslim should always give preference to shaking a Muslim's hand! And regardless of if the Muslim has "washed it" with direct hand contact - that's with his left hand so what's the problem to the non-Muslim? THINK!