I don't know what Kennan was specifically thinking, but the policy of containment did lead the US to fund many liberal/left-wing groups that were not Communist. So the Congress for Cultural Freedom is one case in point, which received CIA funding covertly. This was a group that had pretty far-left politics but didn't think Communism was the way to go. The CIA supported them not because the CIA agreed with their politics, but because they saw supporting anti/non-Communist leftist/liberal groups as a means of drawing away potential supporters who might otherwise see the options as being Communism vs. Conservatism/Capitalism/Right Wing/whatever.

To put it succinctly, if there are more options available to someone sympathetic to liberal values, it makes Communism just one of many alternatives, rather than the alternative. It makes Communism one of the more extreme alternatives at that, since it advocates full-blown revolution as opposed to reform. This was not a fact lost on the Communists — this is why Lenin called them "false friends of the people" as Kennan put it.

One way to think about this is to look at places where the Communist Party USA was influential. In the early Civil Rights movement, for example, they were one of the few organizations that would stand up and be in favor of Civil Rights. So if your options are "be racist" or "be a Communist" you can see that a lot of people would feel the latter was a legitimate option. When additional options are available (e.g. "be anti-racist but not be Communist") suddenly the Communist Party has lost a lot of potential supporters and isn't going to "mainstream" quite as easily.

On CIA funding of the CCF, see Saunders, The Cultural Cold War: The CIA and the World of Arts and Letters. A friend of mine who is working on a book about convert CIA funding of various Cold War liberal organizations has said (perhaps with some humorous exaggeration) that it is hard to find organizations the CIA didn't secretly fund during the height of the Cold War, so eager were they to dilute the potency of the Comintern/CPUSA/USSR. In retrospect it makes for a lot of shocked stories ("CIA funded the Iowa Writers Group!"), though it should be noted that the CIA's hopes were that these groups would keep doing what they were planning on doing anyway (the CIA didn't get strongly involved), and that many CIA-funded organizations did not even know the money was coming from the CIA (the CIA set up "front organizations" that gave out grants for projects they were supporting).

The Long Telegram is actually a very useful document and I think to some extent what you're asking is answered by the document itself. As you've pointed out, Kennan believed the Soviets saw moderate socialists as their biggest ideological enemies within capitalist societies; but just before that he makes another point, that favourable "progressive" political forces - perhaps including those aforementioned socialists - would be the target of Soviet infiltration to be "utilized for Soviet purposes."

When Kennan says "Soviet purposes", he is referring to the ability of the Soviet state to exercise influence and advance its position on the international stage, not necessarily just advancing an ideological position in other countries. I think this phrasing is actually very important because Kennan makes it clear that he believes the chief aim of the Soviet policy is to increase the stature of its own position at the expense of capitalist powers:

"a) Everything must be done to advance relative strength of USSR as factor in international society. Conversely, no opportunity most be miss ed to reduce strength and influence, collectively as well as individually, of capitalist powers."

Therefore these moderate political groups had to be brought on side in the view of Kennan to resist communism, because if they were not then they could either be taken over by communist influences, or outperformed by communist parties in elections. Forgive me for not being more detailed about this part and maybe recycling some of what /u/restricteddata said, but Kennan was acutely aware that Europe was shifting left in tough economic times ("Much depends on health and vigor of our own society"), but it was his belief that if moderate socialists were strengthened, there would be no room for popular far left parties. This would be crucial to preventing the Soviets gaining a political foothold in Europe where they could advance their own position further.

I think you're actually quite close to your answer already with what you know; if you had to boil the answer down to a more simple answer it would be that in European electoral systems, dividing the left wing vote and/or ensuring the left wing vote went to moderate parties would reduce Soviet influence on the selection of governments of European countries, and therefore reduce relative Soviet power. Kennan actually states in the Long Telegram that he fears multiple countries were already under political pressure to serve what he saw as the Soviet's main foreign policy goal, advancing the interests of the Soviet state (As I explained earlier). Here's the quote.

"Where individual governments stand in path of Soviet purposes Pressure will be brought for their removal from office. This can happen where governments directly oppose Soviet foreign policy aims (Turkey, Iran), where they seal their territories off against Communist penetration (Switzerland, Portugal), or where they compete too strongly, like Labor Government in England, for moral domination among elements which it is important for Communists to dominate."

Notice how his chief concern here isn't communist ideology, its "Soviet purposes". I hope my answer will help a bit, I'll try dig out his memoirs tomorrow to shed some light on your second question about what made him think moderate left wing organisations and the Soviets were incompatible. I suspect that he felt the authoritarian system of the Soviet Union (which Kennan said in his memoirs was not representative of the Russian people) would always be incompatible with the European left because the European left valued democracy greatly; he probably believed that they were incompatible not because Europe was moderate left and the USSR was far left, but because one system was democratic and one was the very opposite of democratic.

Sources: Kennan's "Long Telegram" and also his memoirs.

Some historians have examined this period in history as one of a successful 'passive revolution' in Gramscian terms. The belief is that capitalists and their allies in government (both major parties in the USA, for instance) feared popular uprisings of a leftist variety, or even just feared the rise of leftist electoral threats.

In response, they would enact reforms and offer concessions as a way to dull protest, give a portion of what was desired, and in the end, protect the core of the capitalist mode of production and ownership. Think of it as a sort of societal 'flu shot.' There is a potential for endemic outbreaks of new ideas dangerous to your system, so you take a small dose of that, inject it into society, and in the long run, you build a resistance to it, even though there will be changes and side effects.

Passing laws that allowed forming unions, and working with some unions proved beneficial because they would team up to quash communist influence, workers would be less militant, and as a result, there would be less disruption. Indeed, this is what some have called the postwar compromise between the state, capital and labour, which lasted until the rise of neoliberalism in the 1970s. In this way, the last couple of generations have comprised the rolling back of many of the gains workers won as a result of putting legitimate fear into capitalists and their governments.

Reading Antonio Gramsci and others on passive revolution is a good start to understand these views. You may also wish to read Canadian historian Ian McKay, whose work on the Liberal Order Framework can apply to the US context as well.