Avoiding the purging of *communists from the CIO might be a reasonable POD.
Three things made this impossible IMO:
(1) The worsening of the Cold War--and especially its eruption into hot war in Korea. If the CIO had refused to expel its left-wing unions under those circumstances, the government and in particular the NLRB would tilt against the CIO and toward employers or the AFL, and many "right-wing" CIO unions might defect to the AFL. (People sometimes forget that the AFL was *always* larger than the CIO and exerted a constant temptation for CIO unions dissatisfied with the CIO to return to. Among the one-time CIO leaders who had returned to the AFL were David Dubinsky--and for a while John L. Lewis, who even after he had again exited the AFL never returned to the CIO.) Even in OTL, Dave McDonald of the Steelworkers was threatening to pull his union out of the CIO unless it got busy with unity negotiations with the AFL. And of course the AFL would insist on ousting the left as a condition for such negotiations.
(2) Even if there had been less antagonism in US-Soviet relations, the CIO would have gone after the leftists for their support of Henry Wallace in 1948. To non-leftist CIO unions, this was an outrage--the leftists were willing to split the labor vote and risk putting the "Taft-Hartley Republicans" in the White House, just because Truman's foreign policy didn't please Moscow.
(3) Finally, even before the 1949 expulsions, the left wing of the CIO had already been gravely wounded by Reuther's victory in the UAW and by the defections of Joe Curran of the National Maritime Union and Mike Quill of the Transport Workers Union.
I discussed the case of Quill some years ago in soc.history.what-if:
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https://groups.google.com/d/msg/soc.history.what-if/9DXvwSeczjE/zUi1N_JkiC0J
"Red Mike" Quill's break with the Communists in 1948 is indicative of the
way the Communist Party in the postwar years mishandled and lost its
greatest asset, the one powerful social institution where it had a real
foothold--the left-wing unions of the CIO. (I suspect that had Earl
Browder been retained as Party leader in 1945, he would not have been
quite as dismal a failure in this field as his successor William Z. Foster
was--even granted all the "objective conditions" working against Communist
influence in the unions.) The Party insisted that Quill oppose any
increase in the nickel subway fare until after 1949, because defense of
the nickel fare was going to be a key issue in party-aligned Congressman
Vito Marcantonio's mayoral campaign that year. This, even though everyone
knew that the subway lines were losing money and that there was no way
they could afford a substantial wage increase for the workers without a
fare increase. The Party also insisted the TWU support Henry Wallace's
quixotic presidential candidacy; when Quill warned that this could split
the TWU, Foster told him (according to Quill's later account) that the
Party insisted on having the left-wing unions support Wallace even if it
meant splitting every union in the CIO. Quill adopted the motto "Wages
before Wallace" and with his rank-and-file popularity defeated the
Communist majority on the TWU's executive council. He was helped by Mayor
O'Dwyer "who, thanks to a fare increase to ten cents, was able to grant
the union a wage increase that more than satisfied most of the membership.
Moreover, adopting a pattern that would characterize New York transit
negotiations until the mid-1960s, O'Dwyer went through the charade of
appearing to make painful concessions to Quill and allowed Quill to take
all the credit for the wage increase." (Harvey A. Levenstein, *Communism,
Anti-Communism and the CIO*, p. 263)
Quill was also aided by John Santo's voluntarily accepting deportation to
Hungary in 1948. (Santo had previously resisted attempts to deport him,
but now that Hungary was a People's Republic, he imagined a bright future
for himself there, which indeed he seemed to be realizing--until 1956.)
"The union constitution which Santo had drawn up gave extraordinary power
to the secretary-treasurer, the position that he held. His legal problems
forced him to relinquish the position to Gustav Farber, who sided with
Quill and helped to compensate for Quill's lack of a majority on the union
Executive Board." Levenstein, p. 262. The Communists thought that they
could undermine Quill's support among the Catholic transit workers by
proving that Quill himself had been a Communist. Unfortunately for them,
Quill had anticipated them, and had had his membership records stolen from
Party headquarters, even dramatically offering to resign as president if
his CP membership could be proven. (Levenstein, p. 263)
Quill's break with the Communists, coming soon after that of Joe Curran of
the National Maritime Union, was devastating for the left wing of the CIO,
and helped ease the way for the CIO's 1949 purge of the left-wingers...