Learn French: Les adversaires sont forts, mais nous nous opposons à eux. - The opponents are strong, but we oppose them.

With most verbs, "to them" would be leur placed before the verb. However, s'opposer à is a reflexive verb. In French, reflexive verbs followed by à (like s'intéresser à or s'attaquer à) don't take standard indirect object pronouns when referring to people. Instead, the à stays after the verb and is followed by a stressed pronoun, which is eux for a masculine or mixed group.

How would we say this if we were opposing a non-human thing, like a new law?

If the object of your opposition is an inanimate thing or an idea, you replace à + [thing] with the pronoun y. For example, "we oppose it" (the law) becomes nous nous y opposons. The à eux structure in this sentence is strictly used for people.

Why are there two nous in nous nous opposons?

The verb is s'opposer, which is reflexive. The first nous is the subject ("we"), and the second is the reflexive pronoun required by the verb (literally "we oppose ourselves").

If the opponents were an all-female team, what would change in the sentence?