The vast majority of Americans are STILL white, and these immigrants are stuck in cities, and some states. The countryside, the vastness of Pennsylvania, Michigan, Albany, Nevada, Texas is pretty much white everywhere.
It will be more than 100 years that these immigrants will be able to achieve anything in America in population terms considering the size of the American white population, and including the still strong family values among them. They are the biggest evangelist nation on earth, new born Christians.
White Americans still have the highest proportion of babies born in wedlock, much higher than black and latinos, who are the ones to which the social problems, you mentioned, increasingly apply: obscene promiscuity, ultra feminism, substance abuse, disease etc
AIDS is rampant among blacks and Latinos, but not the Whites
And that is ample time for the White Americans to ponder and change. So, you never know, and the scare mongering could be futile.