This is actually a very interesting case study for politics under Stalinism, and how Stalin's ideas moved on from the purely political, the theoretical, to the practical. They didn't so much reject genetics as adopt, for a time, a more politically convenient theory as their view of heredity.

The Soviets, and particularly Stalin, saw the Mendelian idea that competition was the basis for passing on genes as repugnant, because he could not change them as easily, and the parallels to capitalist economic theories were too inconvenient. There was an inherent competitive trait in both. Lysenko proposed a theory that somewhat sidetracked the idea of competition in genetics. It fit with Stalin's and the political establishments ideas on many levels.

If you look at Soviet education theories from the 30s, 40s, and 50s, a period sometimes referred to as "High Stalinism", there was a theory that the minds of children, and to some extent the working classes, were like empty pots. This was convenient for the Soviets as they could create a whole new kind of man through education.

The Soviet Union under Stalin was a place where total political control was not only seen as necessary but also positive in the move towards a true communist state. This idea that total control was a requirement grew into a state of mind where everything could be bent to political control. Including plants, animals, and the transfer of genes.

It went hand in hand with the drive for the new man, sometimes called Homo Sovieticus, where education had to be correct ideologically so too it had to be for scientific theory. The idea that Lysenko presented was attractive to the politics of the time in the Soviet hierarchy. The idea that children, plants, and animals could inherit acquired traits rather than genes were great news because it would make the creation of the New Soviet Man, and his society easier, all the while giving more weight to Soviet political dogma.

It all contributed to the way of thinking in the Soviet Union, and in other dictatorships, specifically the Third Reich, that everything around them could be molded, everything they controlled was plastic rather than hard stone, that with sufficient zeal and obedience, you could bend even the fundamental structures of life to your politics was a gold mine for the Soviet or Nazi regimes. It gave them equal parts motivation, and legitimacy for their actions.

Nothing these regimes did happened independently from politics, nothing happened in a bubble. Everything was tied to politics, and there was some understanding that a good career came with good, aligned with the regime, politics.

But the Soviets also thought it really worked on crops. Initially, the Soviets saw yield increases from Lysenko's theories, at least that's what they thought. But they started trying Lysenkos theories when they also started using tractors and chemical fertilizers. That's where the yield increases came from, but since Lyshenko was a favorite of Stalin, saying so was not only political suicide, but practical suicide too.

Sources include the following:

Iron Curtain: the crushing of Eastern Europe by Applebaum, specifically chapter 13 Homo Sovieticus is of particular interest.

*Savage Continent: Europe in the Aftermath of World War II * by Lowe

The Cold War by Gaddis (not a lot from this one)

Revolutionary Russia by Figes

Just to clarify, I think he's asking about Trofim Lysenko and I'm very curious about this myself. I studied botany in college and am interested in the Soviet Union, and I never quite could figure this out.

This BBC show from a few years ago:

http://www.bbc.co.uk/programmes/b00bw51j

is about that very subject. I found it really to be a fascinating story. I'd say the short answer is that the picture it suggested of reality was inconvenient, ideologically. The guests on the show are estimable experts and explain it much better than I could.