PokéBase - Pokémon Q&A
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Why thanks to both of you who cleared this up for me :)

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No, it doesn't. Rivalry specifically refers to your Pokemon and the FOEs Pokemon of being the same gender.

Hope this helped! GL!

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>Raises Attack if the foe is of the same gender.
- Bulbapedia

So, your allies will not affect Rivalry's affect.
But in a double battle, if the opposing Pokemon are male and female, I think the foe you attack determines Rivalry's affect.

Hope I helped. :)
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