When you’re performing alone at a gig without any band to back you up, you can use the silence to your advantage. Just like a painter painting his/her painting, start with light touches; in other words, use your pick softly. That way, you will have a better control of the dynamics in your performance. To add a little tension to his/her light background, all a painter has to do is use a little darker shade. But if he/she had started with the darkest of the darkest tone it would take crazy intensity to add any shade on top of that. Same goes for the music. If you start very heavy, where are you to go from there? You will have to wrist match with your guitar throughout the rest of your performance. All you’ll get from that would be a few broken strings and an annoying noise. If you’re playing heavy metal music you can get away with that to a point but even a heavy metal song has its dynamics; all the good ones do, anyway.
It’s a common occurrence to play at a gig and face a crowd who is not there only to listen to music. Some might be there to see friends, meet new people, etc. Don’t take it personally.
If you communicate with them well through your music, generally, people tend to get quieter when you bring it down a bit. But even if they don’t, it doesn’t mean you have to fight for their attention by strumming harder. They’ll simply start talking louder as well. You can’t win that battle. Sure, if you have a loud PA system, seemingly, it might help get you heard but it would be too challenging for the listeners to enjoy or tolerate.
Take it easy and play at a level and an intensity that you’re comfortable with at all times.