People are different in their way of understanding the world, and the lenses they see the world through. While my own lense is very much "survival of the fittest", primal, or also known as survivalist. Although with my background in psychology and philosophy, i also understand the more empathic approach (although it's very fun to argue against, definitely guilty there.)
1. Dominantion
2. Survivalist
3. Empathic
For simplicity we will say that these are the main 3 lenses to view the world through. And this is important because termonology and reasoning you argue for with empathic individuals, will be strongly contested against by the other two. And this is true regardless of your main approach of gaining support.
Now one issue you have, is that if you try to adapt for support within all the groups, they all will turn against you, as you've contradicted your statements and been a hypocrite liar.
To gain widespread support in all the groups, you will need to compromise on the terms (wording) used to work in the group you want support. This is often best achieved with support from an individual of another group, that have massive reach, but can also reformulate your message. You need to convince your group, that although there are termonology and changes of words, it means the same, and that all the groups words and definitions relate back to the same origin.
So to prove this i will give two examples:
A man can become a woman. My stance here would be hard "No" and the conversation is over, but i will also push against everything you have ever achieved.
Now on the other side, if you told me:
In human evolution, and because of the nature of evolution there are abnormalites. That can cause some humans to have for example female external organs and male internal organs. Now my response would be "Yes, that is true."
Now your second issue would be wording such as: gender fluidity, non-binary, or "they subscribe to a gender beyond man or woman". The current issue now is that through my lense, man and woman is an abstraction of sex, male and female. You cannot be beyond which means over, or in other cases superior. As my lense is pragmatic and cynical i can also make sense of everything using binary, also known as base2. So if something is "non-binary" is simply do not exist, in the lense i view the world. It does not mean that a person identifying as "non-binary" don't exist, it just means they are either male or female.
If you were to speak to a woman that look through my lense, this is what she would hear if you called her "ciswoman":
For thousands of years, i have been known as a woman. Can you comprehend how derogatory it is when i am suddently called "ciswoman" because of political powers that force me to accept it?
As you might see, from different lenses we use many loaded words. That will create massive backlash if we are not careful. If we return to the statement that i agreed to in the first place. What was as explained is a spectrum, not much unlike skin tones and nuances between white and black.
Of course, it's possible to push for legal actions that work swiftly in your favour in the short term, but that will also create a boiling point, and people who have different political views, will have everything you achieved stripped away at the next political cycle. As they now feel forced, and will happily use force back. So actions such as swift political victories, may actually be a very dangerous idea.
However, generally individuals from the opposite groups, are generally neutral to each other. That neutrality is often confused with "respect".