Is it an act of disbelief for one to say that the fatwa declaring a person an infidel if they do not pick up a paper containing the name of Allah or a verse from the ground is inappropriate for our current era?

Discard these obsessive thoughts. You are not an unbeliever; rather, you are upon Islam. One does not disbelieve by intentionally discarding these papers unless one intended to debase the name of Allah the Almighty. It is not obligatory to pick up every paper found on the ground if doing so causes hardship and difficulty, nor is it necessary to search for and track such items. What you read in that fatwa is not entirely correct, so there is no blame upon you for feeling that it is incorrect.