Calling them "wary of genetics" is a bit of an understatement. Under Lysenkoism they essentially banned Mendelian genetics and embraced a totally separate approach to heredity (one whose rules would change all the time so it is hard to characterize it as anything, but saying that it involved some Lamarckian aspects isn't wrong).

The rise of Lysenkoism is one of these complex historical topics that has a lot of possible answers. In the Cold War it was typically emphasized that Lamarckianism seemed to go better with Soviet ideology (e.g., you can re-form man by environmental forces, are not limited by physical natures, etc.), and there is some aspect of that there, but on the whole scholars who have looked at this seriously have concluded that this is probably a bit overblown as an explanation.

The more careful studies have looked at the political context in which Lysenkoism developed. In the 1920s, Stalin was solidifying his hold on every aspect of life in the USSR, and part of that approach was massive agricultural reform (collectivization). The collectivization movement was a huge disaster, leading to massive famines and crop failures. Simultaneous to this, the Soviet propaganda organs were constantly on the watch for individuals who could be held up as true heroes of the USSR and the physical embodiment of their ideological virtues (the most famous of these would be Aleksei Stakhanov in 1935). Simultaneous to this, there was also a broad push during even the Leninist USSR, but especially under Stalin, that Soviet sciences be re-organized along explicitly practical lines, away from "useless" theoretical musing.

Into all of this comes Trofim Lysenko, a peasant turned agronomist (ticks off the "ideological individual" box) who railed against the useless work of Mendelian genetics (ticks off the "practical science vs. theory" box) and promised new, innovative methods at improving crop yields that were claimed to give huge results (ticks off the "collectivization isn't so bad" box). By himself Lysenko could have been somewhat damaging but for whatever reason Stalin decided that he personally would approve of Lysenko's work at the expense of all others, and essentially made Lysenko the tsar of biology in the Soviet Union. So with the aid of the Soviet presses, Stalin's personal support, and his own zeal, Lysenko essentially worked to suppress Western genetic theories and work in the USSR, and those who opposed him did so at peril of their life.

Lysenko's work was largely charlatanism and obscurantist nonsense, but it fit like a key into a lock of the Stalinist political/scientific context of the late 1920s and 1930s. And once embedded he was hard to get rid of; it would not be until Khrushchev that he was ejected from this role. To be sure, there were ways in which Lysenkoism could be bent to favor a Soviet "re-formable man" ideology (the "theory" was so vague and ill-defined that you can fit it into any ideology if you want to), but it should be noted that under Stalinism, the "official" dogma on philosophy of science (dialectical materialism) essentially says that no science of nature can ever truly conflict or pose a problem to the ultimate science of history/economics (Marxist-Leninism) so Mendelian genetics in this sense was never that much of a threat. From the outside of the USSR, it was very hard to see these complicated domestic political forces at work, though, so a purely "ideological" explanation was both easier to make and also fit with specific anti-Communist rhetoric of the time.

My favorite book on Lysenkoism is David Joravsky's The Lysenko Affair, because he really does a good job in painting the political scene well. Loren Graham's work on Lysenko and Soviet science in general (e.g., in Science in Russia and the Soviet Union: A Short History) is excellent and important. Lysenko is a tricky topic, because ever since the 1930s people in the West have wanted to use it as a "cautionary tale" for thinking about science and politics, and that has resulted in its reality being often quite watered down and bent towards (Western) ideological aims, separating it out of its 1920s-1930s Soviet specificity. (Lysenkoism as an episode is invoked, often sloppily, by people on both sides of the argument about global warming. The "Aryan Physics" episode in Nazi Germany is similarly mangled when turned into a blunt modern-day polemic.)