I recently got a job at NASA writing content for students on websites like Space Place. Luckily for me, astronomy is one of the easiest subjects to get people excited about. I mean, who doesn't like outer space and stars and comets and asteroids and—there is so much cool stuff! There are different levels of interest, sure, and someone can simply appreciate the beauty of the universe without understanding (or perhaps wanting to understand) much of the science behind it, but someone who looks up at a starry sky and doesn't feel a true sense of wonder needs to check their pulse--or blood sugar levels, at the very least.
I think astronomy might be the grandest yet most accessible and relatable field in science. Everyone has access to the sky (although those in cities like me are at quite a visual/light pollution disadvantage), and it's an area of science that non-academics can participate in. It can be a great science hobby—looking through a telescope, maybe even discovering new things and adding to our body of knowledge, no matter where you are.
This is not as true in my background areas of biology and chemistry. If someone said they were a hobby astronomer and had a backyard telescope, I'd say, "That's so cool!" If the next person said, "I'm an amateur chemist, and I have a lab in a shed in my backyard," I'd smile, nod, and back away ever so slowly so that they didn't mail me a bomb.
Seriously, though. I'm not saying there is anything really wrong with being an amateur scientist in any field. I'm just pointing out that few people are amateur chemists, geneticists, or biomedical engineers these days. And if they are, they are assumed to be meth cooks.
The closest thing to being an amateur astronomer would be another area of observational science like bird watching and other such naturalist, rock-turning-over endeavors. That's a science-y hobby with no red flags, but your experiences are local, and people even a few miles away might not be able to relate or appreciate what a nature lover sees, finds, or discovers.
I wish every field in science had the universal appeal and accessibility that space does. I think biology's pretty close, but I'm horribly biased.