"Being a gentleman" covers a lot of territory.
Opening doors for me and then expecting to have sex with me because of it is neither gentlemanly nor going to happen. That type of chivalry is a nicety which is why I TRY TO PRACTICE IT MYSELF. Being nice makes society run better regardless of which gender does it. Having expectations of reciprocation is, at best, naive, and at worst sinister.
Yes, if the pickle-jar needs to be opened and I am not strong enough to open it, I will look around for others who are. Since men are statistically stronger than women, I suppose that is depending on being gentlemanly, but I consider that more an issue of those who can helping out those who can't.
And yes, I frequently help guys with things to make their lives easier, just as I help women with things to make their lives easier. That is part of being a nice person and (to me anyways) just isn't gendered.
Thing is ... I'm not a feminist. I used to be one until I realized that feminists were relishing their victimhood and used the term "equality" only when it could be used to bludgeon society and men into improving things for women, not in any real sense (like equality of responsibility, fixing education for boys, etc).
When somebody opens the door for me, I thank them and then basically forget it happened. There is no "quid pro quo" (other than the "thank you"). And when I do things for other people I don't even expect the "thank you". It's not "doing a nice thing" if it is part of some strange bargain.