Trump should have taken a more diplomatic approach to building this wall. His voter base wants it so he should go ahead and build it. Asking Mexico to pay for it is being stupid, even for a politician, and they way Trump is treating the Mexicans is going to make the rest of the world weary. Mexico should stay strong and it will find better friends, if not a better neighbor.
Trump has complicated the diplomatic relationship between the U.S. and Mexico, this makes the country less safe for Mexicans. The issues of building the wall to keep off illegal immigrants is what has brought this coldness. If Trumps thinks building a wall is the solution, then he should erect it and not force Mexico to fund the project.
The dangers the United States faces because of Mexico are not the result of tension with the Mexican government over an immigration wall. Though not entirely to blame, the failure of the Mexican government to deal productively with drug cartels and gangs in their own country have created real problems for the United States. One only has to look at the problems facing Ciudad Juarez to realize this is the case. However, I do not think Trump's stance about the wall is helping improve relations with Mexico.
No, Trump has not made the U.S. less safe from Mexico. Mexico was never really much of a threat to begin with. The fact that the Mexican president says he will not come to the U.S. for a meeting with Trump makes us less safe from other parts of the world. It's just one more sign of the diplomatic breakdown between the U.S. and other countries.