Some enzymes can transfer a hydrogen atom without lowering the activation energy barrier. how is this possible?

It is true that enzymes speed up the reaction by lowering the activation energy. However, the main concept here is the compatibility of an enzyme to its substrate. This is achieved through lock-and-key theory or the induced fit theory. Either way, the enzymes manipulate the substrates near to the amino acids that can transfer protons (hydrogen ions). This is how it speeds up the reaction.

D-no effect on the rate