Are you asking why Trump didn't try to get Clinton brought up on charges of criminal misbehavior? If so, you can google the words "Lock Her Up" and see that you might have some mistakes about the United States Election process. Or read up on the reactions to the ongoing Russian-Collusion accusations against Trump.
In fact, it appears that during the bulk of the campaign season in the US, both front runners were under separate investigations by the FBI for criminal accusations, with a slew of just wacky out there conspiracies alleging even worse.
Blaspheme laws in the United States do not exist and are in fact banned from existence by the First Amendment, which grants one of the most Liberal Free Speech laws in the entire world... there are hate groups that advocate for lawful genocide of a minority population that are legal under the Supreme Court Ruling (actually instigating unlawful genocide is not legal... and doing so gets you into a lot of trouble.). Candidates are allowed to say whatever they want about any religious figure they want and will not face legal repercussion (Trump said a lot of things about Muslims during his campaign that were not favorable and Clinton was found to hold Catholics in less than high regards as well).
In both cases, neither candidate was an incumbant candidate (though Clinton worked for then Incumbent Barack Obama during his first term and had several friends inside the White House). President Truman was the last U.S. President who was able to run for a third term but was so unpopular by the end of his second, he decided not to run. Since then, all Presidents are limited by two terms for life and Franklin Roosevelt was the only President to win more than two terms (he died in office during his Fourth). As such, President Obama was ineligible from running in 2016 as it was his second term.
As a rule, the FBI will not comment on investigations it is currently working on and will not make arrests or charges of political officials during the campaign BUT that is a tradition and not a rule (Comey definately broke with Tradition when he reopened the case against Clinton and we don't know how it affected her. Most states have "Early Voting" which allows the voter to cast their vote prior to the Election Day, and I believe all polls were opened at time of the announcement, and it was generally a larger than average Early Voting turn out across the board, so a lot of votes had been cast.).
Generally, if a sitting President is running for his second term and uses government agencies against his opponent it's not viewed by the American Public as desirable. The last known time this happened was with Richard Nixon and Watergate. He ended up winning the election legitimately (his opponent was a terrible candidate that lost all but one State and Washington D.C., largely though no fault of Nixons), so he was one of the most popular presidents ever elected... BUT by the time he resigned, he was hated for using government agencies against his opponent and is usually considered one of the worst Presidents ever (if not outright the outright worst).
Basically, even if the President wants to try and use an agency against an opponent, the American People will not stand for it.