Writing the name in red only happened on your family tree record.
When you died, your name, which was written in with black ink, is crossed out with two red lines.
Nowadays the tradition of keeping a family tree record is not as common, but that is where I was told it originates from. Even Europeans kept a family tree, I think, in their bibles. Not sure what they did with people who died though. Did Europeans also cross out the names of people who have already died?
However, a seal is different. Seals are always stamped in red, regardless of what shape the stamp is. One reason for this is because the color red is said to be able to ward off evil spirits, but truth be told, it's just traditional. Same reason why boys don't wear skirts and girls have longer hair. Tradition.
And speaking of weird stuff from Japan:
Squatter toilets.