No, nativists have not abandoned precedents. Instead, they are reacting to Hispanic immigration today in just the same way that nativists have reacted to various other waves of immigration in the past.
In each of the periods in which there has been a great deal of immigration, there have been nativists who have reacted in this same way. The Know-Nothings of the 1850s and those who pushed for immigration restriction in the 1920s did so for many of the same reasons that some people do today. They feared that the immigrants were coming in and failing to assimilate. They feared that the immigrants were causing problems like increases in crime.
The reaction of nativists today is not anything new or precedent-breaking. It is in keeping with reactions to previous large waves of immigration to the US.