I think that many answers to this question are illogical.
The question itself is illogical. It assumes that the problem would be caused by super drug resistant bacteria from the present that have evolved resistance to antibiotic drugs of the present. But as someone has pointed out there wouldn't be any antibiotic drugs in the past anyway.
Instead the problem is caused by the very short generations of bacteria which means that bacterial generations are many times as numerous common as mammal generations - even many times as numerous as mouse generations. So bacteria evolve many times as fast as humans evolve.
So if a person with billions of mostly harmless bacteria in and on him travels to the past and releases some of those bacteria into the environment, those mostly harmless bacteria will have different genes than the mostly harmless bacteria living the past, and will introduce new genes into the bacterial population of the past.
This will change the genetic makeup of many different bacterial species. Changing the genetic makeup of those bacteria species will change the way they evolve in the future. Thus those bacteria species will evolve different new strains and species in the future. Most of those different types of bacteria will be harmless, but some will be deadly diseases. Different deadly diseases than the deadly diseases which would have evolved without the time travel.
Everyone knows that the main influences on how long people live are viruses and bacteria. Time travel would change the viruses and bacteria that people face. Thus time travel will result in some people dying who would have lived, and some people living who would have died.
A person living enough years in the past, perhaps 5,000or 10,000 years, will fall into one of three categories:
1) dies without any children.
2) Has children, but their descendants die out after just a few generations.
3) Has children, and their descendants never died out, but increase both in number and in percentage of the human species year after year, generation after generations, century after century, millennia after millennia, until every single living person is descended from them at least once. And then their descendants will continue to flourish over many millennia as long as Homo sapiens or any biologically descendant species lives.
So if you go far enough into the past, the germs you release will soon cause the evolution of different diseases. Different humans will live or die than would have lived or died without time travel. And some of those who live or die would be ancestors of everyone alive in your era, including yourself. Everyone in your era, including yourself, will disappear and be replaced by an entirely different human population.
A prime example of "grandfather paradoxes".
The Novikov self-consistency Principle and the many worlds interpretation have been offered in attempts to show that there wouldn't be any "grandfather paradoxes" in time travel. But it seems to me that it would take a lot of faith that the universe happens to be structured in a way that makes time travel harmless for anyone to dare to travel in time.
I have ideas for a series about a space/time traveler, and finding ways to make him biologically sterile as far as viruses and bacteria are concerned is vital to making his travels safe for the societies he travels to and their future descendants.
the traveler might be surrounded by a bacteriological "death zone" that somehow exterminates all bacteria within it. Thus he will be incapable of transporting bacteria thousands of years into the past or future of a world. But of course killing all the bacteria that enter the "death zone" will change the the future evolution of their bacteria species and thus the evolution of future diseases.