It will vary by model but our experience is that the only non-sting items are milk, custard, water, and gunge. Everything else stings like hell if it gets in eyes.
I have played with shaving cream for years, hell, decades! It can sting. The best thing to do is clear the eyes before opening. Sounds pretty basic but it works. I don't mean wipe half the foam off your face. Just one finger on each eye from the inside corner across the lashes. Then before you open. Them, squeeze your eyes closed as tight as you can. Then open slowly. Rarely do I ever get anything in my eyes.
Eyes are amazing. The can close in a microsecond. It's your body's way of protecting itself. Its second defense is tears. Rinsing away any foreign material. If you do get shaving cream in your eyes. It stings. Squeeze them tight to get anything out then open them wide and hold them open while it's still stinging. This promotes tears and it rinses the foreign material out. That is the fastest way I have found to stop the stinging. It won't stop the redness but it will stop the irritation.
Whipped cream and cool whip don't tend to sting. I don't like the oily fog they leave on your eyes. For me that bugs me more than a little stinging. That and the sour smell if you use dairy products.
I've gotten the most eye-stinging complaints with chocolate syrup. Not chocolate batter or chocolate pudding, but the super concentrated, fudgy liquid chocolate. Makes sense: if you ever had an ice cream sundae with a pool of fudge at the bottom, that stuff can give a kick to the back of your throat.
Strawberry syrup is similarly vicious to the eyes, so be cautious if you're planning on turning yourself into a '99 icecream! Keep it to the body and you'll be fine.