Smiling is communication. The information content of a message is inversely proportional to its probability. If you smile at strangers in places or situations where that's very unusual, you're communicating pretty strongly, and not necessarily what you intend to communicate.

For example, I live in a part of the world (Northeast US) where the culture is to leave strangers alone. You don't talk to them, smile at them, etc; everyone just does their own thing. If someone here smiled at me out of nowhere, my first reaction would be trying to figure out where I knew this person from, and I'd probably smile back to be polite. Then if they moved on and I really didn't know them I might wonder why they had smiled at me; were they flirting? Visiting from out of town and didn't know the customs? On drugs? Indicating support for something I'm signaling with my appearance or attire?

I can report that nearly half of the strangers will smile back, although often they'll look away as they do.

I'm not sure that's as positive as it sounds? The "look away" part seems to me like it's indicating discomfort, or that they're worried returning your smile will escalate the interaction.

Two questions:

1. How many people have you asked about whether they like it when strangers smile at them, and what has been the breakdown of responses?

2. Where do you live?

I'm a female in the PNW area and notice roughly the same reaction that you describe. I don't smile at absolutely everyone -- I limit it to contexts where it seems unlikely to oblige either party to have additional interactions, although that's still a lot of opportunities. I find that a full-face smile, including the eyes, communicates just fine even in settings where I wear a mask. Then again, my results may be unusual because I present as relatively threatening/intimidating -- I have a family member around my age who gets unwanted conversations routinely even without smiling at people. She is shorter, curvier, better at makeup / generally more normal-woman-presenting, and more agreeable than I am -- I'm not sure which combo of traits is playing into the difference in response. So I'd say that "smile at people more" is safe advice for some-but-not-all women, with who's who being probably determined by nuanced and multivariate factors.

My personal social script for making small talk a more positive experience when I have some superficial interaction with someone, often cashiers when shopping, is to compliment a choice the person has made that day/week. Complimenting something they can't choose (eyes, height, certain bodily proportions, etc) is generally creepy; complimenting a choice they made a long time ago (piercings, tattoos) is hit-or miss; complimenting a small decision that's clearly a recent choice is almost universally a safe positive.

Similarly, shy people can have an easier time making positive small talk with you if you give them something safe to compliment. Accessorizing beyond the absolute minimum, or wearing an outfit that shows you chose it on purpose, gives people who want to say something nice to you an invitation to remark on it.