A cis-political woman is someone who identifies as a woman and / or female, and who is generally more aware of women's issues. She most likely identifies as a feminist.
A cis-political man is someone who identifies as a man and / or male, and who is generally more aware of men's issues. He most likely identifies as a men's rights activist.
A cis-political trans person is someone who identifies as trans-sexual (-female, -male, queer, neither or other), and who is generally more aware of trans issues. They might identify as feminists, men's rights activists, both, or neither.
(The same structure can be used for all gender identities, but for the sake of brevity, only female, male, and trans examples have been used).
A non-cis-political person is someone who is generally more aware of the gender politics that don't relate to their own gender identify. So this includes (but is not limited to) men that are generally more aware of women's issues, and women that are generally more aware of men's issues.
A fluid-political or queer-political person is someone who is similarly well informed about issues that affect women, men, and other gender identifies. They can understand a given situation in terms of how it positively and negatively effects various gender identities. When sexism happens, a fluid-political or queer-political person will feel it similarly regardless of what gender it is expressed against.
Currently, most people with female bodies - even if their gender identify is queer, fluid, non-gendered, undefined, or another option - are cis-political. They are principally aware of women's politics and issues.
There are a lesser number of people with male bodies that are cis-political.
Cis-political is regarded by some as the final frontier of gender fluidity. Whereas many people have made great progress in freeing themselves from the gender roles they were conditioned with, few are able to simultaneously feel the gender experience of all people, equally.
(The author identifies as cis-sexual, does not identify as cis-gender, and sometimes identifies as cis-political.)