InannaEloah said:
Gender refers to "masculinity" and "femininity," both of which are social constructs that have existed for thousands of years and thus is not something that Tumblr came up with, despite some commenters' assertions to the contrary on this thread.

An example of sex: Male. A person who has a penis.

An example of gender: Masculinity. All men like football (no they don't but this is just an example). A man can be feminine by his nature but unless he has an operation he cannot be a female. If a man does things that are traditionally associated with women, he is considered to be a feminine man, or as Arnold Schwarzenegger once put it, a "girly man," for example if a man stays home as "house husband" while his wife goes out and earns a paycheck, he is consdered to be a "girly man." This is gender.

The fact is, gender has been a societal construct for thousands of years. The only people I've ever seen refer to it as anything other than that are Tumblrites, or pseudo-conservative entertainers like Rush Limbaugh who place a much higher priority on being entertaining than on being factual.

I'm going to start numbering the word gender since there are multiple definitions being used and using the same word for multiple things multiple times gets confusing. For the sake of clarity:

gender(1) = the grammar term
gender(2) = synonym for sex
gender(3) = the madeup tumblr ones

Masculinity and femininity are socially constructed, yes, but they are not genders. Masculine and feminine (the nouns, not the adjectives) are genders(1). Male and female are genders(2). Demiboy, aerogender and about 400 others are genders(3).

The most accurate way to determine if someone is male without a DNA test is if they have testicles, not a penis, though people with testicles are almost guaranteed to have a penis.

Gender(1) covers all terms pertaining to a specific sex, such as titles (Mr. and Mrs.), pronouns (He and she), familial relations (Mother, sister, daughter, aunt), etc. and are not negotiable.

People generally say gender(2) instead of sex because gender(1) terms refer to sex and people generally don't feel comfortable saying sex in public due to its other definition, especially around children. In a sense, it's used as a euphemism.

Your explanation of gender conflates gender(2) roles, gender(2) norms and gender(2) stereotypes but doesn't actually define gender(any). Masculinity and femininity are the umbrella terms for those three gendered concepts but are not themselves genders(any).

Gender(3) terms range from treating uncertainty as if it were a separate thing (Demiboy, genderfluid) to things that don't make any sense whatsoever (Aerogender, Ectogender, Impediogender). In my opinion, the word gender should not be used for gender(3) terms as they are all feelings-based and many of them have no relation to gender(1) or gender(2) whatsoever. It's also very annoying seeing gender(3) people arguing with gender(2) people, picking a different term for gender(3) will reduce such arguments.

This list will show you how far off the deep end gender(3) has gone.