It's important to note that LinkedIn, while a social network, doesn't give a full picture of someone. I once overheard a friend say that someone reached out to her via LinkedIn and asked for a coffee and to chat about her work. While my friend was happy to meet up and did, she was sad that she was asked for coffee and not tea. She noted that per her Instagram, all she drinks is tea and that she did not hide her hatred for coffee.
I overheard this while I was in college, and for the most part I don't think people will turn you away for a slight mishap like that — coffee is the most generic networking word for meeting in person. But since then, if I ask someone I connected with on Linkedin to meet in person, I always look at their published work and social media profiles to get a real feel for who they are.
I think my friend would have been overjoyed if someone asked her for tea, her drink of choice, but there's definitely a fine line. Don't get too personal beyond that — like naming their most frequented coffee shop.