CW: I will discuss body dismorphia, or the (seeming) lack thereof I feel when thinking what it would be like to have been assigned the wrong gender. Also I describe sexual roles and thinking about having different anatomy.
Ok, so I've previously read Trans Liberation by Leslie Feinberg and I care about gender insofar as it takes to ensure all gender nonconforming people get healthcare, feel safe in public life, etc. I also will/have changed my language as much as it takes to make my trans comrades feel comfortable. With that out of the way:
I am a cis male, and I guess I am mostly okay with the body I've been given. I prefer to be called him, but I would only be a little annoyed if someone used she/her or they/them to describe me. If I try to imagine my body with a vagina and developing breasts in puberty with my current state of mind, I don't feel very much discomfort. I don't feel particularly attached to the role of penetrating another partner as a gay guy who enjoys bottoming more than topping. If I was forced to wear dresses to church growing up, I don't imagine I would be very distressed.
I do value the relative ease of building muscle that comes with having a male hormonal profile, and I guess dealing with having a female hormonal profile could be alarming, but mostly because it's not what I'm used to. But before puberty, I also wasn't used to having a bunch of testosterone.
On some level, I understand that it can be traumatic to be the target of violence and hate speech, or to be denied medical care. I'm speaking from a position of relative privilege.
Does this mean I'm possibly non-binary? Or something else? I feel content to be assumed as male, but I don't feel that strongly about it. And the title question again, does anybody else who is cisgender or otherwise just not have strong feelings about their own gender?
I feel very similarly to you. I relate at least somewhat to everything you describe. I'm ostensibly cis, but I rarely think of myself as having a 'gender', and I struggle on a personal level to relate to how others think about gender is such strong ways. (And just to be clear, I love and support my trans comrades all the way ).
When I've described this to others in the past, people have just labelled me as 'sort of trans' or 'agender' or 'non-binary', and being assigned these labels makes me a little uneasy, but I understand the motivation (and like you, I'm also wary that I may be speaking from a position of relative privilege). Personally, I've reached the point where I basically present and describe myself as 'male' because it's the easiest thing to do, but as far as a gender identity goes, I don't believe I have one.
I liken it to not really identifying with a name (mandatory mention of P.U.F. <3), you might let others call you by a name for practical reasons, and you can easily call others by their names, but you wouldn't really see yourself as 'having a name'. I let people label me with a gender because it makes life easy, but I don't feel attached to it in any meaningful way. As a social construct I just don't find it useful to view myself through that lens, though I very much understand that others do.