At this point it's such a meme that I'd assume anyone suddenly talking to me in a coffeeshop is doing it because they're a socially anxious person who follows instructions they read on the internet. Not that there's a problem with that, but it's not exactly a strong foundation for a friendship.
The point is to not be some random person you’ve never seen before suddenly talking to you. You don’t start out talking to every person that walks through the door. First you have to establish yourself as “that person who’s always here on Tuesday at lunch”. You don’t do anything other than make eye contact and smile. If someone you see regularly seems friendly and has established a habit of smiling back or nodding when you do then make a point to talk to them if you find yourself standing in line with them or sitting near each other. Just comment on something ordinary like the weather or some nonpolitical event in the news. If you don’t strike up a conversation then don’t force it but be aware of their body language and if they seem comfortable with the interaction then do the same thing the next day you run into them. After a couple interactions you can make a point to say hi to them when you see them next and ask how they are if they don’t seem busy or in a rush. Eventually you’ll strike up a proper conversation and you can introduce yourself by name. After that it’s just a matter of saying hello and asking about the things they express interest in and finding things in common.
It sounds really weird to write it all out but this is just how it works. Familiarity leads to social interaction and you need to be consistent about it if you don’t want it to peter out.
It should also be said that if someone is not comfortable with any stage of this then it’s best to leave them be.
