Welcoming immigrants with open arms is American.
Sadly so is being anti-immigrant. The Alien and Sedition Acts were created less than fifteen years after the Constitution. The Know Nothing Party was a popular anti-immigrant party in the mid 1800s. From then to the mid 1900s were, the Chinese Exclusion Act (1882), The National Origins Act (1924), Japanese Concentration Camps (WW2), Operation Wetback (1954), and those are just the big ones.
The ideals that you have for the US are noble, I hold them too. It’s amazing what the US could be if we (especially our politicians) actually held ourselves to those ideals while addressing our current problems.