I was thinking that given that GW's can be created by the merger of both black holes and neutron stars I don't see why any two colliding objects wouldn't also be able to create gravitational waves, such as two hands clapping. What do people think of this?
I once saw an estimate to the effect that if you spun a nuclear submarine around its short axis at $10^6$ rpm (corrected by Ben Crowell) you would radiate GW having a power equivalent to an ant walking up a hill. So yes, but you get the idea. That's why you need enormous mass acceleration to be able to see anything. Just as knzhou says.
Yes, hands clapping is physically comparable to an oscillating spring as shown here https://ned.ipac.caltech.edu/level5/ESSAYS/Boughn/boughn.html in Figure 1. The spring emits gravitational waves. Note that a time dependent mass quadrupole moment must exist for any system in order to emit gravitational waves. A counterexample would (theoretically) be a spherical symmetric supernova. In this case the mass quadrupole moment is zero. A 'real' supernova proceeds with some asymmetry though.