For myself, I prefer to get their number and call them while blocking mine the first time. Safety reasons. Also lets me call from my regular phone instead of the cell. This could also be why the men are offering their numbers to you, if they have been on line for a bit this is pretty common practice in a lot of areas. If you have had some prior communication through email etc., then block your number, (ask your service provider how if you don't know)go ahead and make the call. If the only communication you have had was them sending you their number, well I would not be so quick to follow up on that if you know what I mean. Once I have had a conversation with someone I generally know pretty quickly if I want to give them mine, or have any other contact with them at all.
Another thing I tend to do is once we have talked on the phone, is to plan a meet up pretty quickly - just coffee, not usually a proper date - after the phone call. I have found that this tends to "keep it real" for both parties, which is very important IMHO. It is far too easy for both sides of the equation to forget that they are dealing with a real flesh and blood human being and for me this tends to keep it real. The coffee meet also cuts down on the "first date nerves" if and when you decide to do that.
I think you are probably just a little nervous about the whole thing, and maybe having an issue about knowing what is proper etiquette in this day and age, which has changed from the last time you were out there meeting people.......and this is a startlingly different venue compared to IRL....
Your phone number lets strangers find out far too much personal information about you, remember they are strangers until you meet.
Is it coffee shops you are uncomfortable with, or just the idea of meeting someone in one?

Oh, and what Chrysalis said.......