It really varies depending on the behavior, and the context. Some things, like holding doors and offering up your seat on the bus to someone who looks like they need it, are seen as good manners/common courtesy, regardless of gender.

Pulling a chair for another man is more complex; it can be seen as courteous (especially if the man is older/has mobility issues) but can also come across as obsequious (like you’re kissing up to him), emasculating (like he’s mogging you, as the incels would say) or presumptuous (‘how dare you assume I need help!’). Egalitarianism and independence are important values for a lot of Americans (at least in theory), so when people act like servants, it can make us uncomfortable; and if we see someone being the target of servant-like behavior, we may perceive that person as entitled or self-important.

Sharing an umbrella with another guy would likely make him uncomfortable, because of the aforementioned independent, egalitarian mindset; it might hurt his pride or cone across as you trying to flex on him (or flirt with him, because you have to be very close to someone in order to share an umbrella, and straight men in America are usually very weird about sharing personal space with other men (the hot tub meme is not an exaggeration). If i saw two guys walking down the street under the same umbrella, I would definitely assume they were a couple, or at least queer friends, because of how weird straight men usually are about this stuff. (And with a female stranger, the gallant thing to do would be to give her your umbrella; offering to share it would likely be interpreted as a ploy to get her within arm’s reach).

As for kissing the hand of the Pope or whoever, that’s seen as very subservient, and a lot of men would probably feel too proud to do it, even if they were Catholics. Because, again, we’re all supposed to be created equal. So even if a guy is above you in the hierarchy, kneeling or kissing his hand on whatever would likely be seen as degrading.

These are generalizations of course; there are always exceptions. As I said, a lot of it depends on context (how well do you know the guy? What’s his position relative to you? How hard is it raining? Will it cause an international incident if you don’t do it?) And because America is so diverse, we don’t really have a monoculture; any or all of these things may be normal for one group and weird in another. Also, I’m not a man. But these are my general impressions, take them or leave them.