Is this true? I've never heard of women working on California railroads, and her description seems vaguely racist, as it was an example of how East Asian peoples are "particularly gracile".
it's hard to prove a negative; I would like to see your professor's evidence. That said, the majority of Chinese immigrants were male. Many women accompanied professional husbands. There were also enslaved prostitutes who were imported, although their number can be overstated. I have never heard of this claim that Chinese American women "passed as men to work in the American railroads," and given that there were so many other options for women in general in the American West, I doubt that this happened in an significant numbers if at all.
One of the best sources I have encountered on Chinese American women in the West is an excellent essay by Sue Fawn Chung in a collection of essays I co-edited: Ronald M. James and Elizabeth Raymond, Comstock Women: The Making of a Mining Community (1998).
Let's be generous to your professor here and assume that she just doesn't know very much about the history of American stereotyping of Asians.
For your initial question, I don't know of any Chinese women who dressed as men in order to work in male-dominated railroads. That doesn't mean it didn't happen: there are plenty of cases of women who pass as men that pop up around history, such as the first African American female soldier, Cathay Williams. She served in the Union and went by the name William Cathey, survived the war and then worked as a farmer in Colorado and Texas afterward. However, a large number of women choosing to pass is unlikely and certainly unknown.
As for immigration law, women could freely enter the United States until 1875 with the Page Law. The law was written to prohibit "prostitutes" from entering (a standard of respectability that later European female migrants had to deal with as well, as some unaccompanied women from Europe were refused entry) but the explicit intent of its author was to prevent Chinese women from entering the United States. Your professor's assertion that exclusionists wanted to prevent "breeding" is correct (and also expressed as most exclusionists expressed themselves, bluntly) but not complete. It was a one-two racist punch: the first was to protect the morality of white men by preventing the entry of prostitutes, and the second was to discourage the formation of permanent communities by Chinese migrants, which of course happens when whole families are able to lay down ties in an area and raise children. Actually, there wasn't as much agreement about Chinese exclusion during the 1850s, 60s, 70s, and 80s as there seems in retrospect. George Peffer's important book on the Page Law quotes the attitude of many on male Chinese migration: "If They Don't Bring Their Women Here," then Chinese men will not set down permanent ties and become American, so their mass entry is acceptable.
The Page Law's restrictions were implemented by the American consul in Hong Kong, and later by customs officials at entry points. Basically, officials assumed all Chinese women were prostitutes unless they could "prove" otherwise. Women did this by exhibiting class-based signals like buying first class tickets on ships, bringing portraits of themselves in fancy silk clothes surrounded by rich furniture (as befitting the lifestyle of merchants' wives that American officials looked for), having bound feet, displaying literacy, etc.
Male migration continued unimpeded until 1882's Chinese Exclusion Act, which balanced the desires of racists who wanted blanket exclusion, businessmen looking for ties to Chinese markets, and people uneasy with the cutting-edge and totally unprecedented limit on movement across and within borders. Diplomats, merchants, students, and the family members of people already in the US could enter. From that point on the government kept ratcheting down the ways that people could enter and the rights they were entitled to once they arrived.
Still, if someone was a student (Christian missionaries sponsored women to study in the United States), a family member of a person already in the United States, or a merchant or diplomat's wife, she could enter.
But I think one problem with your prof's answer is that it assumes that nineteenth century people were not very perceptive. For one thing, it assumes that whites were easily fooled about a Chinese person's gender because of their body type. While the average worker on railroads was quite short -Iris Chang claims about 4'10" and 120 pounds, though I've seen different estimates I can't find right now - that doesn't mean that other indicators of gender such as facial structure, mannerisms, speech patterns, voices, etc would have been disregarded. Chinese men were required by the Qing government to wear a queue - a long ponytail with a shaved forehead, which women would not necessarily have had. Plus enough women had bound feet that the probability of one without bound feet, coming to the US at the right moment, with enough physical ambiguity that she could pass as male, without any ties to people who knew her so that she could pass - all of this adds up to unlikelihood.
Even if all that were true, whites were not insensitive to different kinds of Chinese people even though the anti-Chinese exclusionists tried to paint them all with the same brush. Actually, whites were extremely interested in distinguishing laborers from merchants, and (in the 1850s-1880s, or into the 20th century for some Christians) what some whites looked for was the ability of a person to demonstrate "American" qualities. Here's a quote from a newspaper in Washington Territory, the Puget Sound Argus in 1876 after a man named Ah Jay purchased farmland for $1250 in gold:
"This shows that Ah Jay is patterning after our American style of farming - casting away the hoe and taking up the plow. He means to pay his taxes as other farmers and make the country his home. Jay is quite an intelligent looking man."
Americans were also able to distinguish between Chinese, Japanese, Filipino, and other Asian migrants. Most famously Teddy Roosevelt strongly endorsed Japanese society as admirable and civilized. I'm not saying there wasn't stereotyping amongst whites, because there certainly was. But it was more of a push-pull between the exclusionists who wanted to dehumanize everybody equally, and people of varying motivations who wanted to distinguish people more finely.
These distinctions became more blurred over time, until the mid-20th century when you have kind of a catch-all "Asian" stereotype. This man has yellow skin, slit eyes and a pigtail and says "ching chong" and mixes up r's and l's. That stereotype is actually a conglomeration of Chinese, Korean, Japanese, and others and it isn't what nineteenth century Americans were thinking when they stereotyped Chinese.
Well there was a deliberate effort to stop Chinese women from immigrating. See the Page Act of 1875. The racist (and untrue) sales pitch behind the clauses about Chinese women were that they were all prostitutes and would lower the morals and purity of white men. In reality it was another effort to stop the growth of the already small and extremely gender imbalanced Chinese communities in America. They wanted to keep the cheap labor, but keep the communities from growing and offending the electorate, so they made it practically impossible for women, wives and families to come over. Obviously race-mixing was illegal, so they thought their policy would work- and it sorta did.
When it comes to emasculation and the sort of belittling orientalism academics still tend to have about sex, you gotta turn to history. Without women, Chinese men had to do "women's work" like running laundries and serving as the help. Laws and racial norms made it very difficult to do anything else. And of course the image of Asian men without wives furthered the image, which persists today. Also the Qing dynasty manchu-style long braids didn't help either.
Now whether or not Chinese women posed as laborers to get around all the restrictions and live in America? I'm doubtful.