Why do the men wear oxygen helmets in "A Sound of Thunder"?

The men wear oxygen helmets so that they do not introduce modern germs into the ancient air.

When the men visit the past with Time Safari, Inc., they have to be very careful not to affect the environment in any way.  Even the smallest change could have a drastic effect on the prehistoric ecosystem.  This is why they carefully place a path to walk on and only shoot animals that are just about to die....

The men wear oxygen helmets so that they do not introduce modern germs into the ancient air.

When the men visit the past with Time Safari, Inc., they have to be very careful not to affect the environment in any way.  Even the smallest change could have a drastic effect on the prehistoric ecosystem.  This is why they carefully place a path to walk on and only shoot animals that are just about to die.  This is explained to Eckels, the hunter.

"We don't want to change the Future. We don't belong here in the Past. … A Time Machine is finicky business. Not knowing it, we might kill an important animal, a small bird, a roach, a flower even, thus destroying an important link in a growing species." 

Proof of this occurs when Eckels accidentally steps on the butterfly.  Seeing the dinosaur scares him, and he chokes.  He isn’t even able to kill it himself.  Travis makes him collect the bullets.  They can't leave anything behind.

As they are leaving, Eckels is so out of sorts from the experience that he accidentally steps off the path and kills a butterfly.  When they return to the future, it is clearly a different future.  The sign’s spelling is different and the wrong man was elected president.  He looks at it in disbelief.

It fell to the floor, an exquisite thing, a small thing that could upset balances and knock down a line of small dominoes and then big dominoes and then gigantic dominoes, all down the years across Time. Eckels' mind whirled. It couldn't change things. Killing one butterfly couldn't be that important! Could it?

Travis murders Eckels in retribution, but the damage is done.  If killing one tiny butterfly caused all of that change, can you imagine what several minutes of breathing into the air would have done?  When you breathe out, you breath out germs that your ecosystem is used to.  The age of the dinosaur would not have had the same germs.