Ok, I can answer this as this has happened to me several times (although never quite that direct).
[Actually, first let me say I strongly think you should approach men. Most of the guys you really want aren’t sitting on OLD month after month unable to meet women. ]
In any case, to your question about married guys...Initially it’s flattering and I tend to be a bit of a flirt / chatty which can kind of encourage it.
That said it begins to be obnoxious when you know I am married and keep persisting.
The personal trainer who kept asking me to meet her mom and hang out on Thanksgiving even after I said I was spending the day with my wife and her family.
The Starbucks barista, who’d met my wife many times, repeatedly asking where I lived so that she could bring me my mobile orders (I place it on my phone and walk over and pick up my order).
The waitress at the bar across the street who would constantly bring me free drinks “this one is on me” (but never bring any to my wife). If things were slow she’d come sit with us and chat.
The bartender (different bar) who asked to borrow my phone when my wife went to the bathroom. We’ve known her at least a year. I thought she was going to google something...nope, she put her number in then texted herself my number and said “now we have each other’s numbers.” She has texted her work schedule to me many times in the past couple months in case I want to have some drinks and chat.
So, yeah, some guys are taken. But, I’m never mean to the women- especially the ones who bring free drinks! :)