Regular dishwashing soaps and laundry detergents that doesn't have the mark "Antibac" or "Antibacterial". Because if it can't...then doesn't that mean that you have been wearing unclean clothing (although, cosmetically, it looks clean) and eating off dirty plates for your whole life?

Yes soaps and detergents can kill some bacteria but very few if any viruses. Don’t forget the main reason we wash clothes and clean plates are to remove the shed skin and food (respectively) that the bacteria grow on. It is also worth pointing out that almost everything we interact with has some bacteria living on them (including our own skin). The vast majority of these organisms do us no harm and we happily live with them. Thus the term “clean” plates or clothes is a relative thing!

May I add that the important part about hygiene is not to get rid of all the bacteria around and live in a sterile environment. This actually could be detrimental to your mental and physical health. The point in hygiene is to get rid of the bigger part of the bacterial population to remain under a pathogenic dose of bacterial intake. Most pathogenic bacterias are harmless at low dose. As David pointed out viruses are another story.