Electrostatics?

The part of them being able to exert gravitational force on each other is correct.

A body is electrically neutral if the net charge it carries is zero. That does not mean that they have no charge, - just no net charge. If the positive and negative charges are separated from each other within each body, they will exert a net force on each other.

To see this is a very simple scenario, consider two bodies marked red and blue below (I can't draw a figure right now - so you will have to imagine the different colored brackets as two different bodies!)

#color(red)((+ qquad -))qquad qquad color(blue)((+ qquad -))#

Here, both bodies are neutral overall. The red negative charge will repel the blue negative charge and attract the blue positive one, and so on. Here, there are four pairs of charges - each either causing an attraction or a repulsion. While the number of attracting pairs is equal to the number of repelling ones, the attraction between the red negative and blue positive charge is much more than the rest (since they are a lot closer - the inverse square law!). Thus, the two bodies will attract each other.