Do you understand that words can have different, multiple and even conflicting definitions and a dictionary merely represents how words are used?

For reference, Miriam-Webster's defines woman as such[1]:

Your opposition isn't to the definition of "woman" but the definition of "female":

    adjective
    1. a (1): of, relating to, or being the sex that typically
              has the capacity to bear young or produce eggs
       (..)
       b: having a gender identity that is the opposite of male

    noun
    1. a: a female person : a woman or a girl
       b: an individual of the sex that is typically capable of
          bearing young or producing eggs

But these are clearly two different meanings of the word "female": one based on reproduction and another based on gender identity. So there is no contradiction in saying that a "woman" can be a person with a female gender identity who does not meet the reproductive definition of "female".

Note that it also defines gender identity:

    noun
    a person's internal sense of being male, female, some
    combination of male and female, or neither male nor female

Additionally it helpfully defines gender itself:

    noun
    (..)
    2. a: SEX sense 1a
       b: the behavioral, cultural, or psychological traits
          typically associated with one sex
       c: GENDER IDENTITY

For completion's sake here's the definition of sex it references:

    either of the two major forms of individuals that occur
    in many species and that are distinguished respectively
    as female or male especially on the basis of their
    reproductive organs and structures

So "gender" can refer to reproductive characteristics, gender identity or "the behavioral, cultural, or psychological traits typically associated with one sex". Note that this says "typically associated with" not "inherent in" as these attributes are all mutable and vary. It also provides a helpful usage guide for the differences between "gender" and "sex" because the distinction can be confusing if you never had to think about it much.

In other words, it's not actually "redefined the word 'woman' to include males", it has merely added nuances that better reflect how the word is used in practice. Note that the definition of "sex" is also handwaving a lot of the complexity (e.g. by saying "typically" a lot) because in practice it's better described by this humongous chart:

https://www.scientificamerican.com/article/beyond-xx-and-xy-...

Note that a lot of the stuff in the bucket of "intersex conditions" can be easy to miss when sex is assessed at birth and what the person looks like as an adult is determined by a number of hormone washes starting before birth and only ending after puberty. You can say "oh but these are exceptions" but 1) so are trans people and 2) exceptions need to be considered if you care about a definition being correct.

It's also interesting that you seem to focus on the existence of trans women, not trans men. Male puberty (i.e. testosterone) is much harder to "undo" than the opposite. You have the choice between the absurdity of calling someone like Shawn Stinson[5] "a female" and insisting that he must use the women's restroom or acknowledging that if you didn't know he is trans, for all intents and purposes outside intimacy he is obviously a man.

[1]: https://www.merriam-webster.com/dictionary/woman

[2]: https://www.merriam-webster.com/dictionary/female

[3]: https://www.merriam-webster.com/dictionary/gender%20identity

[4]: https://www.merriam-webster.com/dictionary/gender

[5]: http://4.bp.blogspot.com/-y3cdHPl_hdw/VZTTItWC6yI/AAAAAAAA0K...