What if MNIST dataset had another feature
Convolutional layers are useful for images because they take into consideration the neighborhood of pixels. However, for labels like gender and handedness a convolutional layer may not be particularly useful. 

However, after the convolutional layers you usually tend to place some densely connected layers. It is there that you may want to add these additional features. When you reshape the 2D matrices which results from the convolutions, you can concatenate the additional features, then feed this new vector to your Dense layer.