At least officially, it is not really accurate to say that we accept all people who want to come to our shores in the way that Emma Lazarus’s poem suggests that we do. This was much truer at the end of the 19th century than it is today.
Lazarus’s poem was more appropriate in the late 1800s when there was essentially no limit on immigration. The US accepted practically everyone provided that they were healthy and they were not completely destitute. Thus, huge numbers of relatively poor immigrants were accepted into the United States at that time.
Today, we are less welcoming. We have much stricter limits on how many people may enter the country. In addition, we have many more people who would like to come and so we are much more worried about being overrun by large numbers of immigrants. Because we now have laws about immigration, we do not legally accept as large of a percentage of the “huddled masses” that want to come to the US. We see many now as illegal immigrants and threats to our future.
Thus, our attitudes have clearly changed since Lazarus’s poem was placed on the pedestal of the Statue of Liberty.