Isn't it redundant to use "then" after "if"?

I would not consider it redundant to have if...then...

Leaving aside the point of using then to clearly mark where the consequent clause begins, the use of both if and then can serve to emphasize the causal nature of the antecedent, or to make it seem like an if and only if rather than just an if-then.

For example:

If it rains, we will stay inside.

merely provides the plan of action in the case that it rains, whereas:

If it rains, then we will stay inside.

seems to suggest that the staying inside will only happen if it rains (note the emphasis on then, which would be stressed in speech and italicized in writing).