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If you cast protect and fortune on a unit of shining spears does it then become 2+/3+/4+ save?

Fortune isn't a saving throw, so doesn't benefit from Protect.

 Mr. Shine wrote:
Fortune isn't a saving throw, so doesn't benefit from Protect.

This is the correct answer.

As mentioned, Protect and Fortune do not have any interaction whatsoever. However, casting both on Shining Spears would indeed make them tough, giving them a 2+ Armour, 3++ against shooting and after those fail, you'd get a 5+ roll to ignore damage (rolling 1 D6 per damage dealt)