Short answer: you can do anything you want forever.
Slightly longer answer: if you think that your life would be improved if you changed some part of how you look, act, present yourself, or think about yourself, then you can make those changes piecemeal. You don't have to start identifying as something new just because you want to change your name, pronouns, clothes, or hormonal makeup; all of these things can exist independently of each other, and you are free to choose exactly who you are. Also important is that this is not exclusively for queer people, nor does it make you inherently queer! Non-queer people have to learn the lesson at some point that they are also free to explore their genders without judgement or restrictions, and it's perfectly possible to, as a bare minimum example, identify as cis while using different pronouns.
The principles of gender anarchy are inspired by those of relationship anarchy, a concept we learned about from our sister, and realized worked very well for us. The basis of relationship anarchy is to not strictly categorize personal relationships, and to be open to whatever form a relationship may take, whether platonic, romantic, sexual, and/or something else. This shares DNA with polyamory, but we would argue that polyamory is often a consequence born from engaging in relationship anarchy in the sense that more than one relationship may be romantic at the same time. In the same spirit, gender anarchy is about not strictly labelling and categorizing gender and gender expressions, and instead embracing that gender is a personal thing and it's every individual's right to express theirs in the way they prefer at any time. There should be no connection between the terms you use, your pronouns, your body, your clothes, or anything else commonly considered to be gendered.
Gender is an oppressive force in our current culture, and is enforced harshly. Cis people perform gender harder than any trans or gender non-conforming person I know. The lengths cis people will go to stay within the limits of their gender identity are frightening, and even the most educated cis people start feeling personally attacked or threatened the moment their gender is challenged in any way. This is why they often find queer people threatening too; their existence suggests that the boundaries of the gender binary are permeable, that they never had to abide by such strict (self-imposed!) rules, that they can't judge people on the basis of their gender, and of course anything that challenges the status quo is scary and dangerous.
This is why gender anarchy is important; the more we can de-emphasize gender as a cultural divider, the less we can make our lives restricted by our genders, the better.
More questions?