I study in singapore and I have non-muslim friends. I naturally meet a lot of non-muslim people too.
My concern is that all non-muslims, well, don't wash after they use the washroom... and some dont even wash their hands. And many a times, I do come in contact with my friends and have handshakes with people. I try washing my hands if I do but it gets inconvenient at times.
So should I be concerned about this? Am I being too conscious? Is there any kind of teaching regarding this in the quran or hadith?