Can gravity ever be a repulsive force?

You are mixing together the concepts of antimatter and that of objects having negative mass. The latter has never been observed, but works by physicist Hermann Bondi and others show that there is no necessary contradictions within the concepts, as long as you formulate it properly.

Antimatter, though, is generally assumed to have positive mass.

https://en.wikipedia.org/wiki/Negative_mass

 

This is a hairy question, because when you start treating Gravity properly, it cannot be classified as an attractive or a repulsive force. In fact, even calling it a force requires qualifications and a coordinate system choice.

If you take just a step back in complexity to consider linearized gravity, yes, there are repulsive gravitational effects even without such a thing as negative mass. These involve gravitomagnetic effects. Two masses moving at high velocity in parallel will experience gravitomagnetic repulsion. But just like with magnetism, this can be viewed as simply a reduction in gravitational attraction. The net force is still attractive.

As for gravity being repulsive in strictly Newtonian sense, that would require a negative mass, and arildno's post covers that.