I think all of us kind of imagine the worst case scenario in our head. The situation where somebody at the coffee shop sees the website you're browsing, spits out their coffee and yells, "What the fuck website are you on right now?? Look at this guy, he's talking to suicidal people!!"
It's unlikely that it's ever actually happened how I described, but my anxiety-riddled brain jumps to that conclusion whenever I'm out in public.
Based on my experiences with people, I don't know if they're really paying that close attention. There are people who come into the coffee shop where I work at everyday, and I've never once glanced at their computer screens to see what they're looking at because I just assume they're studying. It's also too far away to see from behind the counter, so I don't even bother snooping.
And to be honest, if I saw somebody looking at suicide methods on their laptop in public, I'd raise my eyebrows a little and be like, "Wow". But even then, I'm not certain why they're on the website—they could be doing research for a college paper or something. I also don't want to start a conversation with a random stranger, so I'm not going to say anything anyway.
Outside of family, who else is really going to give a shit? A lot of us are suicidal in the first place because of people not giving a shit, so can we assume that most people would just walk on by, say nothing at all, and think nothing of it? And is there anything anybody could realistically do to us if they had a problem with it?