I have been going out in public occasionally as a man in a dress/skirt. I am not interested in being "more" feminine than that. I'm just a dude.
I live in the southern part of the United States where conservatism (morally and/or politically) is supposedly more common.
I have observed society's reactions change from years ago when people would whisper to their friends and hide a laugh, to people taking a look and moving on.
Teenagers used to try to whip out a phone and get a picture. I don't see that any longer. Teenagers are no more likely to pull out a phone than an adult. It is rare that I see it.
I have observed people go from having "oh, that's unfortunate" conversations about LGBT things in the old days to now where there is a LOT more hate in their rhetoric. But never when a crossdresser is around.
Most people (whom I assume are never around people like us) seem to feel awkward, not knowing what to say/do. If I speak first and say, "Good Morning." or something normal like that, they respond appropriately. I think it is similar to how one would react to meeting a handicapped person or a person with significant scars or facial tattoos. "What do I say/do? Where do I look?"

At first, I would go to remote, unpopulated places to crossdress in public. For example, take a walk around a park at night. In an effort to be "safe" I did some rather risky things -- risky no matter how I was dressed. I also went to clothing stores. I was always alone.
I found it very fulfilling once I was able to do things that I would do as a guy, but while dressed pretty: Christmas shopping, air travel, eat lunch, grocery shopping, and go to church. I think my favorite activity has been going grocery shopping. You see the same people again and again for 30 minutes. Eventually, they stop feeling awkward and they might even talk to you occasionally. It's nice. I think that the grocery store is nice because it is very common for someone to be alone.

Going to church was pretty good, because while I am there, I think I could create relationships with people. I have gone to church maybe five times. I have gone to a liberal church and a very conservative church. I have gone to Seventh Day Adventist churches a few times because they meet when I don't have a scheduled church service at my normal (men's clothes only) church. Church doesn't rank up there with the Grocery store because I think I still feel like I might be unwelcome, so I am apprehensive. So far, however, no one has made me feel unwelcome. In fact, at the very conservative church, I was made to feel the most welcome.

Do people care? I don't even know what that means.
Are people decent? Yes.

Caveat: I don't go to biker bars, places with children, Trump rallies, Florida, or anywhere else that might have an unpleasant outcome if I showed up. (OK, I went to Florida once.)