Generally speaking, when I write characters of different genders I firstly make a point of viewing them as people first, man/woman/agender second. The moment you let a character be defined first and foremost as A Woman (Or A Disabled Person or A Black Person, etc), you've already blown it. For example when a man writes a female character badly it's usually because of a poor ability to empathise and also because he has made the mistake of placing far too much emphasis on the fact that she is A Girl. Which is why he keeps focusing on her boobs and ladyparts and outfits and makeup and periods and blah blah blah instead of giving her a damn personality, which should have been his first priority. (It should ALWAYS be your first priority with every character you write).
But that aside, it's not a good idea to ignore the fact that gender makes people different from each other in fundamental ways. Mostly, I would say, because people experience the world differently depending on their gender. So while I give all my characters the same range of emotions, I do it with the awareness that they're likely to respond to and express those emotions differently.
For example, I wrote about a man whose background and upbringing were pretty traditionally masculine, who is dealing with the tragic death of his son. Like anyone would he becomes depressed and traumatised, but he deals with it by being surly and standoffish with people and trying to drown his grief in bourbon, and angrily rejects the idea of asking for help or even accepting any comforting from other people who offer their sympathies because he subconsciously thinks that would be "weak". When he finds his son's suicide note later on and a friend is consoling him, he of course feels the need to cry but suppresses it. It's obvious enough that growing up he was taught the mentality that "men don't cry". So he bottles up his emotions and it ends up doing him harm. If this character had been a woman, she would probably have been much more inclined to be open about her grief. I have another character who's a woman who is very physically strong and fearless, but she still has feminine traits such as a motherly side and a tendency to cry when upset.
Of course this is all fairly broad; there's absolutely going to be a whole lot of variations (eg I also have a male character who's shy and sensitive and who isn't afraid to shed a tear). But that's the basic idea.
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But that aside, it's not a good idea to ignore the fact that gender makes people different from each other in fundamental ways. Mostly, I would say, because people experience the world differently depending on their gender. So while I give all my characters the same range of emotions, I do it with the awareness that they're likely to respond to and express those emotions differently.
For example, I wrote about a man whose background and upbringing were pretty traditionally masculine, who is dealing with the tragic death of his son. Like anyone would he becomes depressed and traumatised, but he deals with it by being surly and standoffish with people and trying to drown his grief in bourbon, and angrily rejects the idea of asking for help or even accepting any comforting from other people who offer their sympathies because he subconsciously thinks that would be "weak". When he finds his son's suicide note later on and a friend is consoling him, he of course feels the need to cry but suppresses it. It's obvious enough that growing up he was taught the mentality that "men don't cry". So he bottles up his emotions and it ends up doing him harm. If this character had been a woman, she would probably have been much more inclined to be open about her grief. I have another character who's a woman who is very physically strong and fearless, but she still has feminine traits such as a motherly side and a tendency to cry when upset.
Of course this is all fairly broad; there's absolutely going to be a whole lot of variations (eg I also have a male character who's shy and sensitive and who isn't afraid to shed a tear). But that's the basic idea.