A, because the experiment is repeated with boiled ginger juice, milk can't solidify at any temperature, which means that there are active substances in ginger juice, which can inactivate it at high temperature, so it can be proved that fresh ginger juice contains an enzyme that can transform soluble milk protein into insoluble state, so A is correct;

B, at low temperature, the activity of the enzyme is low, but the molecular structure of the enzyme is not destroyed and the activity is not lost. Only at the high temperature of 100℃, the molecular structure of the enzyme has been destroyed and lost its activity, so B is wrong;

C. If ginger juice and milk are mixed without heat preservation, the temperature will change frequently. Therefore, mixing the same amount of ginger juice with milk at different temperatures can improve the accuracy of the experiment, so C is correct;

D, 60℃ and 80℃ are not necessarily the optimum temperature for the enzyme, but it may be completely solidified within half a minute at 70℃, so the optimum temperature can only be obtained by narrowing the temperature range and increasing the temperature gradient, so D is wrong.

So choose BD.