The first two answers focur on the idea that this is EXCLUSIVE language -- it does not allow women or nonwhites. But this is also INCLUSIVE language. It DOES allow all free whites to become citizens.
This is important because it shows America as a nation that is going to welcome immigrants and is going to end up being built on immigration and the melting pot. The people who wrote this law would have felt this way partly for ideological reasons (all men are created equal) but also for practical reasons. We needed more free white people to build our population, spread out across the land that we took from the Indians, and make the US strong economically.
This is not a surprise simply due to the time period. Things were very different back then. Free white men were in charge of the country and that is just the way that it was. People still owned slaves so anyone who was not white was viewed as being beneath them and certainly not an equal. The intent of the Naturalization Act was to limit who was allowed to become a citizen.
It was also limiting to women because the act stated that citizenship was inherited through the father. In other words, if a woman was a citizen of the US but the father was not and she had a child born abroad that child would not be a citizen of the US.
It was not until the 14th amendment (post Civil War) was passed that ALL people born in the US were granted citizenship. It was not until 1870 when people of African descent were granted naturalization.
Such language should not be surprising for a variety of reasons. The first reason would be that the framers' or the founding fathers were unable to fully grasp the issue of race and racism. Whether this was done deliberately or out of pure ignorance or a combination of both is something that can be debated. With this in mind, the framers or those in the position of power did not see the issue of citizenship as something applicable to those individuals of color for in their mind, being a person of color was seen as being either a slave or a Native American, already perceived to be a threat to land and territorial possession. I don't see the exclusion of people of color as a surprise for it is a part of the canvass of American History. For a nation that spoke the loudest on the issue of inclusion and acceptance, its history represented some of the most stunning examples of its antithesis.