The short answer is that a good deal of global public opinion labeled the Germans as the aggressors for acting first. Anglo-French commitments to Poland only pertained to German aggression. The language of the treaty was vague, containing references to a "European aggressor", but all parties generally understood the language to be directed at Germany. The timing of the Soviet invasion threw Allied foreign policy into disarray with some in the French and British government and public sphere calling for anti-Soviet actions up to a declaration of war, and others adapting a wait and see approach hoping for the German-Soviet rapprochement to collapse. Most of the Anglo-French decision makers favored the latter policy, as expanding the war to the USSR would drive the Soviet-German relationship closer when it was in Allied interests to drive it apart. For their part, the Soviets portrayed their invasion and subsequent annexation as a return of a lost territory (the Western Ukraine and Western Belarus) or a proactive protection of the region's peasantry from the exploitative landlords. Soviet propaganda often mixed the two rationales, generating more confusion.
The Soviet Union's public image paid dearly for this invasion. Despite the presence of a few true believers abroad, a good many Communists and leftists outside the USSR saw the Molotov-Ribbentrop pact as an ideological betrayal. Much of the global left expected the German invasion to lead to a resuscitation of the Popular Front of the 1930s. The French Communist Party's deputies voted for emergency war credits on 2 September, a position its leadership had to backpedal after the Soviet invasion. The Comintern tried to propagate the rationale behind the Soviet invasion, but the damage was done. The organized left either became estranged from the USSR or ideologically incoherent in their defense of Stalin's actions. A number of party members left the Party as a result, and the Soviet actions in Poland gave license to a crackdown on Communist Parties and their publications throughout Western Europe. The Soviets would not regain this moral high ground until Barbarossa as the Nazi's portrayed the invasion as an ideological crusade against racial inferiors.
Over the winter of 1939/40, advocates of a military response against the USSR gained some traction in light of the stalled Soviet war against Finland. There was some preliminary French military planning for airstrikes against the Soviet oilfields of Baku and in December, the British war cabinet authorized the sale of military equipment to Finland. But plans for a more substantive military intervention never really got off the ground. Range limitations of the current generation of RAF and Armée de l'Air bombers made Middle East-based bombing of Baku quite difficult. The British cabinet was quite split over Baku, with hawks like Churchill favoring bombing or the threat of bombing to cow the Soviets into not making oil deliveries to the Germans while Chamberlain feared an empty threat would only prompt the Soviets to beef up the Baku air defenses. Soviet breakthroughs in Finland likewise rendered military assistance to the Finns moot.
One of the important dimensions of these anti-Soviet plans was that they were designed as a form of economic warfare against Germany. Even intervention in favor of the Finns had an important component of trying to sway neutral opinion in favor of the Allies. So while attacking the USSR's aid to Germany was militarily out of reach, an intervention in Scandinavia was not. Again like in Finland, facts on the ground put an end to these schemes as the Germans simultaneously anticipated a Scandinavian operation. There was some debate in London and Paris as to whether after Scandinavian they would be in a better position to threaten the USSR with real or feigned military intervention to stop its supply of raw materials to Germany. The Norway debacle and the Fall of France rendered this debate moot since Britain would have to prioritize using its armed forces against Germany and her Italian allies.
The lee-way granted Russia in this matter was a matter of timing and practicality. Because Russia waited until the matter had been decided by Germany in the west of Poland before themselves crossing the border, they were able to present the thinnest veneer of justification that they were acting in defense of the Belorussians and Ukrainians who had been citizens of Russia before the Treaties of Brest-Litovsk and Versailles. What's more, the strategic situation compelled France and Britain to acknowledge the occupation of Polish territory by the Soviet Union as an evident fact, even if they were not entirely happy about it. On the whole, their public reaction was molded by the recognition that it was currently beyond their power to aid Poland against the Soviet Union.
They therefore deferred action under the pretense that Poland had not invoked their mutual treaties against the Soviet Union as they had against Germany. As reported by the New York Times, the general attitude in London was such that any action against the Soviet Union was thought to be a “quixotic gesture that would be far from helping Poland and would weaken the Allies’ chances of victory and restoration of Polish and Czech-Slovak independence.”^1 In the interim, their policy continued as before: Britain and France sought to prepare their armies, their industries, their populations and their finances for what they expected to be a grueling war of attrition in the West.
Deference to the reality of occupation was not, however, a signal of approval. The leader of the Labor Party, Arthur Greenwood, was quite staunch in his commitment to a war fought with the ultimate aim of securing Polish independence, no matter who might challenge it. He said, “the British working class movement has adopted a definite, unalterable attitude against aggression, wherever and by whosever it is committed. It has accepted the challenge thrown out by Germany. It will not now turn its back on the Polish people, who are the latest victims of aggression, alas on two fronts.”^2 Although they were resigned to the temporary subjugation of Poland by the combined act of Germany and the Soviet Union, The Times of London reported that “public opinion here is revolted, though not the least dismayed, by these cynical exercises in lower diplomacy.”^3 Stalin’s opportunism was looked down upon by the British and French, but at the time they remained focused on their primary enemy: Germany.
Nevertheless, the allies would intimate that their patience for Soviet expansionism was not limitless. On the 10th of January 1940 Neville Chamberlain referred to the Soviet Union as “that power with whom Germany made an unholy pact and to whom she set the example of aggression.”^4 In the same speech he praised Finnish resistance against the Soviet Union as being conducted in the same spirit of liberty and justice for which the British fought. Two months later the New York Times reported that Britain was weighing war against Russia should the Finns prove unable to resist them, an assertion which was buoyed by a statement that if it were requested Britain and France would “proceed immediately and jointly to help Finland [with] all the available resources at their disposal.”^5 It may well have been an empty promise given their current preoccupations, but such statements make clear the fact that Soviet adventurism was not going unremarked upon.
Because neither Britain nor France had the power to oppose the Soviet presence in Poland, they made a cynical choice for themselves to do nothing and say little, so as to better preserve the chance of victory against Hitler. While this is hardly a positive act on their part in defense of Poland, it by no means constituted approval of the Soviet Union’s behavior. Because they were unable to win the fight if they were to seek it, they prudently restrained themselves.
I've already talked about this here:
https://www.reddit.com/r/AskHistorians/comments/542utc/if_the_united_kingdom_was_legally_obliged_to/