Although some of the mandatory powers I get (such as Anti-Matter) --- does having them as Mandatory take out some of the strategy and diplomacy? What if I don't want to pillage a hand as the Barbarian or smash more ships as the Cudgel, etc.?

The Mandatory nature of the alien is sometimes its trade-off for having such a strong power- certainly the case for Anti-Matter. It's just part of the overall hand management aspect of CE... you KNOW you have this mandatory power, so you have always account for it, and you have to plan ahead. Yes, Cudgel doesn't want to smash so many of Masochist's ships... so, he should only attack with 1 or 2 ships, and pick a planet that has very few of Masochist's ships there (to mitigate the effect).