The hydrogen protons undergo quantum tunnelling in the the sun to fuse into helium, but are only able to do so as they are under immense heat and pressure and the protons and electrons get separated. But our digestive system also makes use of quantum tunnelling to quicken the digestive process, but how do the enzymes free up the electrons when our body temperature is so low?
The probability of quantum-mechanical tunneling through a barrier depends on the energy involved in the barrier. For two protons to fuse requires overcoming an energy barrier of many millions of electron-volts. By contrast, energy barriers to configuration changes in atoms and molecules are typically a few electron-volts or even a fraction of an electron-volt.
Quantum-mechanical tunneling can occur in enzymes at room temperature because the energy barriers are comparable to thermal energies at room temperature, a few milli-electron-volts.
I don't know much about digestion, so I'm not sure about which biological process you're referring to. That said, the tunneling probability only requires energies which are significant compared to the energy barrier. The sun is trying to fuse nuclei together, and the energy that binds nuclei together is huge. So it takes a lot of energy and very high temperatures. In chemical situations, the energy that binds an electron to an atom or molecule (or the energy that binds atoms together) can be millions of times lower than the energy barrier present in the sun. So it's not necessarily surprising that chemical-energy tunneling processes can occur at room temperature.