Born with a penis and in possession of a Y chromosome.
It's fairly obvious 99.99% of the time if someone is a man or a woman just by looking at the face.
My 7-year old can tell the difference also, without pulling down the pants or doing a DNA test.
To the ideologists, they don't mean anything, that's for sure. "Man" or "woman" are just masks in their thinking. The funny thing is, they think they're defending trans people with that junk but it just makes things worse. A lot of us find it totally stupid and wish this crap would go away. A man is an adult human male and a woman is an adult human female. It's not an "identity". I don't "identify" as a man. That's just part of who I am. I'm Frank. Transsexuals are people with a medical condition and are better off living as the opposite sex to which they were born. The exceptions don't destroy the rule. Obviously it's based in biology or else transsexuals wouldn't exist in the first place!
It is true that most people identify with a gender matching their birth sex, so in most cases, it is safe to assume that a person is the same gender as what their physical appearance (male or female) indicates. I also believe that gender is not entirely socially constructed: it seems to have a biological component too. Just how much of gendered behaviors and traits is biological and how much is socially constructed is the question. I don't have a definitive answer, but if I had to guess, I would suspect around 70% was socially constructed and around 30% was biological.
However, where the definition of "man"/"woman" as "adult human male/female" starts to show inaccuracy is when we look at adult human males/females whose gender doesn't match their birth sex. If we define a man as an adult human male, does that mean that trans men aren't men? Or that non-binary biological males are men?
An analogy that I find quite useful about gender compares the notion of gender to the commonly recognized biological group of fish: the latter are not a formal taxonomic group in biology, but most people still recognize them, and the classification is useful in practice. Similarly, there is no rigorously defined list of traits that delineate each gender, but we can still recognize who is a man or a woman (in terms of gender, not sex) in most cases.
I don't think it is ideological or biased to say that each gender has no rigorous list of defining traits. This is a mere acknowledgement of current science. What would such a list look like? In Saudi Arabia or Yemen, strong jealousy toward one's partner is typically associated with "masculinity," while shyness and timidity are typically associated with "femininity." There are a lot of differences between the traits associated with each gender in, say, the US or the UK and in Saudi Arabia or Iran.
I disagree with the notion that gender has no biological component whatsoever, but I also disagree with the notion that it doesn't have a significant socially constructed and culturally variable aspect.