It’s like learning how to drive and you have that feeling like if every honk of horn is directed at you. In reality most people don’t care.
For the few that do care, usually around sensitive areas (Police Departments and Government agencies), it helps to have a good appearance. Nobody wants a creepy person looking like they’re taking upskirt shots. Dress clean and dress well. Shoot away and don’t mind others.
Most people will be like “Oh, it’s a photographer doing photography stuff, that’s why they’re walking around this small area and standing funny”. Pretend you own the whole area. It’s yours and everyone else is just there because you allow it.
During the learning phase of photography, start off with a small camera or a smaller lens. You’ll be less intimidating while you learn. You’ll see the pros lugging around tripods and huge telephoto lenses because they’ve learned to not give a crap. but you don’t have to start there.
Visit places you don’t typically go. I’m a lot more self-conscious taking photos where I live because there’s a good chance I’ll see these people again. If I’m a tourist, there is about ZERO chance, so I care far less about seeming awkward.
Be in your own world and care less about others. Go out with more of a who gives a crap attitude and take photos you want to take and damn any person who thinks that it is weird or laughs for whatever odd reason.
Also Read: 100 things to learn about photography
Ultimately, keep shooting. Eventually, you’ll be comfortable around others.