People should be chivalrous to each other, not just men to women! I am a woman, and I hold the door for whoever is coming behind me coming in! Man, woman, child, dog.
I don't ride public transportation often, but I would only offer a seat to someone who was elderly or injured or looked like they needed it, or maybe someone wearing unsensible shoes :~)
It's not necessary to offer your seat to someone in hiking boots or tennis shoes, should be the rule.
Good point. Good old-fashioned respect and consideration for others gets dropped by the wayside all too often anymore, and that goes both ways.