For the record, I consider "dude" to be gender neutral ;)
IMO, no, you're not being inconsiderate. The nature of online discourse means that gender is generally a lot less relevant unless it is inherently a part of the topic being discussed - which is how it should be IRL as well. If we were in public, however, and I had spoken with you and told you the pronouns I wanted you to use, and presented as female, and you still used "he/him" for me, I'd probably be seriously uncomfortable.
The most important thing to do? If you don't know - ASK. I have never met a trans person who would be more upset by you asking their gender than they would be by you getting their gender wrong. And if you mess it up the second time around, just correct and don't make a big deal - We're way more scared than you are.
I do think it's a good case of due diligence to look up some of the linguistics behind trans stuff, just because It's not really going away any time soon so far as i can see. So, like email and internet and cell phone, it's something we all have to learn. the same thing might become the case if the community and/or english scholars can decide on what gender neutral pronoun to use (probably singular they because our language already sort of supports it - like taking advantage of a weird compatibility in a program).
So here's a basic rundown on some stuff that, if you know, makes wading through conversations
Transgender person - Someone whose gender differs from the one their doctor put on their birth certificate.
Trans(gender) woman - Someone who previously used he/him pronouns who now uses she/her pronouns. That person could have been assigned male by their doctor at birth, or possibly had unclear genitalia at birth and was raised as a male. Regardless, they now will likely be going by female pronouns.
Trans(gender) man - Someone who previously used she/her pronouns who now uses he/him pronouns. That person could have been assigned female by their doctor at birth, or possibly had unclear genitalia at birth and was raised as a female. Regardless, they now will likely be going by male pronouns.
genderqueer - One of many words used to describe people who don't feel strongly as either male or female. An example might be someone who dresses very androgynously and uses they/them pronouns.
Cisgender - Cis is the opposite of the latin Trans - Cisalpine Gaul, for example, meaning the area of Gaul on the Roman side of the Alps, and Trans Atlantic meaning across the Atlantic Ocean. A Cisgender person is someone whose gender is the same as the one the doctor put on their birth certificate. That means that a cisgender man will likely, but not exclusively have XY chromosomes and a cisgender woman will likely, but not exclusively have XX chromosomes. Chromosomes, and genetics, are complicated.
I mean, in a perfect world gender wouldn't be a factor in how we talk about each other. Men and women would exist perfectly equally. Trans people would still exist, but their taking of hormones to change their body wouldn't be a social issue, just a private one.
However, we don't live in that world. We live in a world where we put people into boxes because humans like little tidy boxes. Turns out that the world of human gender doesn't fit into our two box system of male and female, or even into some other cultures' Three gender box (though more boxes is likely better). So we are currently at a cultural turning point where we have to deal with trans people again. It's happened before (see the Weimar Republic for a recent example), and our choice has been to sweep trans people under the rug - Hopefully we can prevent that from happening again and start to change the way we look at gender.
Hope some of this helps.