In programs like Photoshop you can preview your design using color blindness filters (View > Proof Setup > Color Blindness). Another trick is to grayscale your design to check the contrast. This will help a lot to create a design that is also accessible for colorblind people.

Contrast is the key here. Red for example is a very dark color. That's why they use to print secret documents on red paper. When you would copy such document with a copier it would become completely black.