At typical physiological pHs glutamate does exist as glutamate.
Broadly the acidity in the digestive track is enough to reduce glutamate to glutamic acid. The stomach for example has a healthy pH of between 1.5 to 3.5.
Canadianer points out in the comments that the active site during catalysis are protonated. There are obviously a lot of examples of this and sensitive evaluation by looking at the isocontours and surface potential of the protein structure are needed to draw conclusions if this might be important.