conservative with little to no logic or critical thinking? = rightwing nutjob
liberal with little to no logic or critical thinking skill? = SJW/regressive left = Tumblr idiots (not all Tumblr users, just the idiot ones)
Those that would be against it anyway are against it anyway, because they just don't want to understand. In the case of those that are open to ideas beyond their current knowledge, I'd say the Tumblr mentality have turned off a lot of people to being open about social changes. They poisoned the pool by being self-righteous morons who are as racist and sexist as those they purport to fight against. That and most people will have heard of the...curious people who "feel they are a wolf all in but the way they look", and think this might be an extension of that. Obviously it's not, but people can only work with what they know.
Sex and gender are very different things, where sex is genetic and usually based around male and female(xy, xx, respectively). Though xxy, and many other genetic disorders, can present themselves as non-binary, generally speaking it is in their relationship to male and female chromosomes that the genetic discussion takes place (as genetics deals with heritage and the passing of genetic material). While rare, these genetic variations can easily be considered different sexes and that would relate to the gender discussion.
Gender is separate from sex, though is related, and is a matter of self-understanding with relation to one's culture. If in your culture, and you, think a girl is defined by wearing dresses and makeup and acting a certain way, and you wish to do all those things, you would likely identify your gender as a girl. Or perhaps you have traits that you would consider male, and other parts you consider female, and other parts that are neither. What then? Well, if these traits are important enough to you that you feel they define who you are, then, you may feel you do not belong to the "male" or "female" categories. Take how other people perceive you and how you've been taught genders are "suppose to act" (culture), and add how you perceive yourself, and you wind up with a lot of genders. a lot.
Orientation is independent of both, more or less.
If your world-view consist of "got a penis? Man. got a vagina? woman.", then it gets confusing real quick, especially when people call you sexist/threaten your life/etc for not knowing something and supporting something without ever hearing about it previously. It's rough out there. There are a lot of racist/sexist/etc aholes out there, but some people just express confusion through anger and resentment. Childish perhaps, but not necessarily racist/sexist/etc.
Also note I glossed over a few things and oversimplified others. The genetics can be more complicated, and the gender can be more complicated, but I figured I had rambled on long enough. For the record, to each their own. Express who you are however you want, just don't hurt anyone else in the process and you're good. Got my support.