It depends on the ride. On something smooth and comfortable like a B&M hyper I can definitely relax. For example, Candymonium at Hersheypark is a great ride to practically ragdoll on. Also, putting hands up is a good start even if you're tensed up. When you realize on some level that holding on isn't doing anything but letting you tense your muscles unnecessarily you'll start to feel more freedom on rides. Also, as you become more familiar with ride forces, you can better predict how upcoming elements will feel and you can brace for them in a more relaxed way, rather than trying to stay totally rigid in your seat
Not a coaster, but on an S&S screamin' swing I notice that I tense up totally involuntarily. Something to do with the amount of airtime and the feeling of the restraint. It really depends on the ride.