I'll specify the timeframe to around the 1880's-1900's, when organized labor movements such as the Knights of Labor and the American Federation of Labor began organizing and advocating for workers rights in the industrial sectors such as Coal and Steel.
Were elements of these upstart labor movements aware of or read up on Marx and his Communist Manifesto that was being discussed among European intellectuals? If so, what was their take on the manifesto, especially as it applied to the work environment they were advocating reforms for?
Many of these 'upstart labor movements,' as you call them, were reasonably well-read in socialism and Marxism as it was developing in the latter half of the 19th century. However, as I will lay out below, neither the AFL nor the KOL were especially receptive to Socialism and frankly the Socialists of the era weren't especially in too deep to ideology either.
Firstly, the Knights. The KoL is commonly understood to be a 'labor organization,' but to be frank it really wasn't in the modern sense. The KoL was a broad-based working-person's fraternal organization, and something of a nascent broad-based union, but it really wasn't an organized labor movement. Indeed, the KoL is best understood as being a transitionary body, and it
served as a bridge between what might be called the pre-modern, and distinctly localized labor organizations that preceded it, and the modern and more nationalized or international (meaning the United States and Canada) form of organization that followed it. [Dubofsky 93].
The KoL retained a sizable urban contingent, for sure, made up of low-skilled workers ignored by larger trade unions and craft organizations [Sanders 51] but an inability to protect striking members or leverage it's strength lead to a precipitous decline in urban areas. It is perhaps best to think of the KoL as an attempt to formalize a nascent agrarian-labor alliance so often sought in America. The Knights was perhaps 50/50 between urban and agrarian contingents, which made socialism in the KoL essentially a nonstarter - for socialism tended to denounce, more than support, farmers and populists. A Socialist Labor Party declaration in 1893, for instance, noted that Farmers represented a
hybrid and transitory class that is doomed to dispossession and disappearance through the action of economic forces evolved by a modern system of production.
The story of Daniel De Leon is perhaps most illuminating in regards to the KoL's relationship with labor. New York city was a hotbed of socialist strength in the late 19th century (85%+ of the Socialist Labor Party's votes came from New York State in the 1892 election [Leip]) and De Leon was one of American Socialism's early leaders. However, the Knights weren't necessarily receptive to Socialist ideology -
After taking control of the SLP, De Leon set out to use his New York Socialist base to gain control of the Knights of Labor. With the aid of the city's United Hebrew (garment) Trades and other Socialist-led unions, De Leon got himself elected delegate to the 1893 KOL General Assembly from New York's DA 49 [...] When [KOL leader] Sovereign refused to appoint De Leon's SLP ally to the editorship of the KOL journal, the New Yorker "declared war on the Knights." By 1895 tensions had reached the point that members of the De Leon clique were refused seats at the Knights' General Assembly. De Leon then ordered the thirteen thousand members of the unions he controlled to leave the KOL.
Not exactly friendly.
The AFL, meanwhile, was a far more urban labor-heavy organization than the Knights (which arguably undercut it's strength but that's a story for another time) and thus would theoretically be more receptive to Socialism than the agrarian-influenced KoL. However, the AFL was also founded as a surprisingly conservative organization initially dominated by Craft Unionism - oft denounced as 'business unionism.' The AFL at it's founding was
Steadily opposed to the formation of an independent labor party [...] [and] viewed the idea of the welfare state with suspicion and actively lobbied only for legislation that would permit trade-unionism to make effective use of it's economic power through organizing, through collective bargaining and through the use of the strike [...] it made no serious effort to increase its political strength by alliances with progressive groups outside the fold. [Karson 285-286]
The AFL actually was quite opposed to the Socialists as a bloc, being 'old rivals;' it emphasized 'pure job consciousness' and strongly emphasized 'voluntarism' as opposed to broad based (socialist) organization of the working classes. Indeed, the AFL was a narrow organization for much of it's early history, dominated by skilled craft workers. The AFL shaded gradually into "business unionism, and "labor for itself" became "each craft for itselfm" [Sanders 77], and the entire organization was gradually roped into the agenda of capital. However, with the decline of the Knights and the failure of the Socialists, and with the gradual opening of the Federation to more broad based unionism, things would begin to shift - and though it's theoretically out of the scope of your question, I'd like to draw attention to a noteworthy statistic. The AFL was hardly insulated from socialists, and
the Socialists even amassed one-third of the voting delegates at AFL conventions by 1911 and controlled a number of the affiliates. [Dubofsky 95].
Sorry for taking a month, hope this answered your question!
Citations:
Marc Karson, American Labor Unions and Politics, 1900-1918.
Elizabeth Sanders, Roots of Reform.
Dave Leip, 1892 Presidential General Election Data - National.
Melvyn Dubofsky, American Labor: a Documentary Collection.