If you travelled sufficiently into the future (or indeed past) is it not quite probably you would encounter diseases for which you had no immunity? Same as native people (historically related to us just 100s/1000s of years ago) never had immunity to our new European diseases?
The Time Machine would be far more realistic if he got off his fancy vehicle (described by Penny as "something Elton John would drive throught the Everglades"), and while trying to chat up some fit Eloi bird, broke down into a coughing fit covered in black **** pustules.
Needs revised along with Mad Max imho. Did the Eloi need toilet paper? We'll never know.