I think you're right - I think that's a
Culcita sp. cushion star, most likely
C. novaeguineae. If I'm correct with the ID, there's some good news and some bad news.
The good news is, they are super cool stars: they are surprisingly flexible despite their cushion shape, and harlequin shrimp don't seem to be interested in eating these guys at all.*
The bad news is that they are confirmed corallivores, eating corals like Acropora, Pocillopora, Monopora, and Pavona for certain (it confirmedly doesn't like Porites).
C. schmideliana is also known to eat Galaxea, Goniopora, and Xenia, so I wouldn't be surprised to find if the star eats most corals. They also are known to eat some small inverts, such as urchins...
I haven't heard any complaints about them with snails or shrimp yet, but that doesn't mean they're entirely safe (though these guys are known to have symbiotic relationships with a shrimp species -
Zenopontonia soror - a fish -
Carapus mourlani - and a polychaete worm -
Gastrolepidia clavigera - so they might not be too hard on inverts).
*The study that offered these guys to harlequin shrimp: