Before I bought my first electric vehicle in 2012, I told myself, “I don’t want to switch from burning gas to burning coal,” since coal at the time was the biggest portion of my electric utility’s fuel mix. I went ahead and bought my 2012 Chevy Volt, because I installed enough solar panels on my home to get all my electricity from the sun. Since then, I have bought three Teslas and sold one (my RWD 2014 Model S to friends in Arizona).
Then I learned why EVs have lower emissions than gas-powered cars, even if the fossil fuels represent 100% of the utility’s fuel mix. The reasoning is reflected in this graphic from http://www.FuelEconomy.gov:

The gist of the graphic is that only 16 to 25% of the energy in gasoline goes to propelling the vehicle. The rest is basically waste energy, 68% to 72% of it engine losses such as heat. By contrast, roughly 90% of the energy in electricity goes to move an EV.
That differential in fuel efficiency is at the heart of why EVs are more climate- and pollution-friendly than gas-powered vehicles can ever be.