the.com/lace curtain

The thin, see-through line between poor and pretending not to be.

means Describes a style of respectable, aspiring-middle-class status (especially among Irish-Americans) marked by genteel manners and a determination to seem a cut above one's rougher origins.

from From the literal lace curtains hung in windows — a cheap, lace-making-machine-era way to dress up a modest home and signal refinement to the street. The phrase 'lace curtain Irish' emerged in American English (roughly late 1800s–early 1900s) to distinguish upwardly striving, decorum-minded Irish immigrant families from the unflatteringly-labeled 'shanty Irish.' The curtain itself became shorthand for the whole performance: thin fabric, thinner pretense, hung up for the neighbors to see.

origin
19th-century slur for upwardly mobile Irish immigrants
vs shanty irish
distinguished by furniture, not actual wealth
function
let light in, kept the neighbors' judgment out
legacy
became shorthand for status anxiety, not fabric
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