First, it is worth noting that the "Deutsche Physik" movement was actually mostly a failure. Their major success was briefly harassing Heisenberg and getting one of their people appointed to a professor position as opposed to a better person. After that they sort of fell apart, because the actual Nazi leaders were not all that sold on their argument and realized that having good, world-class physicists was more important for their war aims that prosecuting ideological battles of this sort. One of the major proponents of the movement, Johannes Stark, only very narrowly avoided being sent to a camp because he became a critic of the Nazis (they weren't Nazi enough for him) and had a nice house that a military officer desired. Seriously! (See Mark Walker's Nazi Science for the best discussion of the movement I have seen.) Which is only to say: don't overestimate the centrality of it to the Nazi's ideology or overestimate its success. People often do, because it makes the Nazis seem even more ridiculous than they are, but this is bad history.

But to your main question — how was ideology in physics handled in other countries? In the USSR there were philosophers who attacked relativity as being "bourgeois physics" that went against the doctrine of materialism, because it seemed to imply that "all was relative" and "truths aren't true" and etc. (It doesn't, really, but this was and still is a popular way to talk about it.) There were other physicists who worked to reformulate relativity in a way that would avoid this kind of attack. Vladimir Fok, for example, insisted that relativity was just a "theory of gravity" and removed all potential philosophical content from its discussions, reducing it to just equations. Another physicist, Boris Hessen, attempted to use history as a weapon here, showing that while Einstein himself was certainly bourgeois and of a bourgeois culture, the favored physics of the anti-relativists — Newtonian physics — was no less reflective of its own totally non-socialist context (Newton's 17th century England). Thus, Hessen argued, you can't really say Einstein's work is more bourgeois than Newton's.

In the end, the thing that gave the physicists "security" was not these kind of philosophical arguments, which raged back and forth during the dangerous years of Stalin, but their utility to the state. The Soviet nuclear weapons program in particular gave physicists a practically unprecedented level of "safety," to the point that at least one of them (Sakharov) could later become even a dissident and for a long time be somewhat tolerated. Which is to say, as with the Nazis, the practicality of physics "won out" over ideological arguments. On this, see Loren Graham, Science in Russia and the Soviet Union: A Short History, which discusses both Fok and Hessen I believe.

I know less about physics and ideology in China, but there were cases of it cropping up. Specifically the Chinese rejected the Big Bang, because they viewed it (like many people did at the time, including some scientists in the West) as being essentially religion/creationism wrapped up in scientific language. They preferred a steady-state cosmology (the universe is endlessly old, etc.) that didn't feel like it had a "beginning." The astrophysicist Fang Lizhi came under a sustained campaign against his advocacy of Big Bang cosmology in the 1970s. (As an aside, the entire physics department at the school where Lizhi taught was sent to work in a coal mine during the Cultural Revolution — the issues of ideology and Chinese science go deeper than the content of the science, because during the 1960s university professors were seen as potentially being of a "rightist" class that needed "reeducation" generally.) On this episode, see James H. Williams, "Fang Lizhi's Big Bang: A Physicist and the State in China," Historical Studies in the Physical and Biological Sciences 30, no. 1 (1999), 49-87.

In all of these cases, it should be made very clear that these opinions were rarely handed down from "on high." That is not generally how state ideology in science works, with a few exceptions (Stalin, for example, sometimes did intervene idiosyncratically in some debates). A better way to think about it is that ideology creates a sort of loose power that permeates everything — it creates a resource that can be seized upon and used to various ends. The Deutsch Physik practitioners, for example, sensed that they could take beliefs they already had, tweak them a little bit, and have them appeal to the Nazi state, and by doing so get ends that they desired (professorships, suppression of opponents, etc.). That worked a bit, until it didn't. The philosophers in the USSR used Soviet ideology as a weapon against all comers (and themselves), part of a sort of literal academic deathmatch where the only way to avoid getting purged was to try and purge others first.

In the long run, all of the cases of ideological science were only successful against fields that could not prove their utility in some way, and thus make themselves useful to the state. Chemistry in the USSR, for example, did not suffer much — it was obvious that the chemists did important things, and the chemists deliberately emphasized their value in this way to make sure they didn't get wrapped up in ideology. Biology in the USSR, by contrast, couldn't deliver results for Soviet problems (like famines and crop failures), making them especially vulnerable to fast-talking charlatans who could promise fast action (like Lysenko). People who worked on modern physics appeared vulnerable in the 1920s-1930s, but the discovery of nuclear fission in particular gave them quite a bit of "insulation" against sustained political attacks on the content of their work.

First, it is worth noting that the "Deutsche Physik" movement was actually mostly a failure. Their major success was briefly harassing Heisenberg and getting one of their people appointed to a professor position as opposed to a better person. After that they sort of fell apart, because the actual Nazi leaders were not all that sold on their argument and realized that having good, world-class physicists was more important for their war aims that prosecuting ideological battles of this sort. One of the major proponents of the movement, Johannes Stark, only very narrowly avoided being sent to a camp because he became a critic of the Nazis (they weren't Nazi enough for him) and had a nice house that a military officer desired. Seriously! (See Mark Walker's Nazi Science for the best discussion of the movement I have seen.) Which is only to say: don't overestimate the centrality of it to the Nazi's ideology or overestimate its success. People often do, because it makes the Nazis seem even more ridiculous than they are, but this is bad history.

But to your main question — how was ideology in physics handled in other countries? In the USSR there were philosophers who attacked relativity as being "bourgeois physics" that went against the doctrine of materialism, because it seemed to imply that "all was relative" and "truths aren't true" and etc. (It doesn't, really, but this was and still is a popular way to talk about it.) There were other physicists who worked to reformulate relativity in a way that would avoid this kind of attack. Vladimir Fok, for example, insisted that relativity was just a "theory of gravity" and removed all potential philosophical content from its discussions, reducing it to just equations. Another physicist, Boris Hessen, attempted to use history as a weapon here, showing that while Einstein himself was certainly bourgeois and of a bourgeois culture, the favored physics of the anti-relativists — Newtonian physics — was no less reflective of its own totally non-socialist context (Newton's 17th century England). Thus, Hessen argued, you can't really say Einstein's work is more bourgeois than Newton's.

In the end, the thing that gave the physicists "security" was not these kind of philosophical arguments, which raged back and forth during the dangerous years of Stalin, but their utility to the state. The Soviet nuclear weapons program in particular gave physicists a practically unprecedented level of "safety," to the point that at least one of them (Sakharov) could later become even a dissident and for a long time be somewhat tolerated. Which is to say, as with the Nazis, the practicality of physics "won out" over ideological arguments. On this, see Loren Graham, Science in Russia and the Soviet Union: A Short History, which discusses both Fok and Hessen I believe.

I know less about physics and ideology in China, but there were cases of it cropping up. Specifically the Chinese rejected the Big Bang, because they viewed it (like many people did at the time, including some scientists in the West) as being essentially religion/creationism wrapped up in scientific language. They preferred a steady-state cosmology (the universe is endlessly old, etc.) that didn't feel like it had a "beginning." The astrophysicist Fang Lizhi came under a sustained campaign against his advocacy of Big Bang cosmology in the 1970s. (As an aside, the entire physics department at the school where Lizhi taught was sent to work in a coal mine during the Cultural Revolution — the issues of ideology and Chinese science go deeper than the content of the science, because during the 1960s university professors were seen as potentially being of a "rightist" class that needed "reeducation" generally.) On this episode, see James H. Williams, "Fang Lizhi's Big Bang: A Physicist and the State in China," Historical Studies in the Physical and Biological Sciences 30, no. 1 (1999), 49-87.

In all of these cases, it should be made very clear that these opinions were rarely handed down from "on high." That is not generally how state ideology in science works, with a few exceptions (Stalin, for example, sometimes did intervene idiosyncratically in some debates). A better way to think about it is that ideology creates a sort of loose power that permeates everything — it creates a resource that can be seized upon and used to various ends. The Deutsch Physik practitioners, for example, sensed that they could take beliefs they already had, tweak them a little bit, and have them appeal to the Nazi state, and by doing so get ends that they desired (professorships, suppression of opponents, etc.). That worked a bit, until it didn't. The philosophers in the USSR used Soviet ideology as a weapon against all comers (and themselves), part of a sort of literal academic deathmatch where the only way to avoid getting purged was to try and purge others first.

In the long run, all of the cases of ideological science were only successful against fields that could not prove their utility in some way, and thus make themselves useful to the state. Chemistry in the USSR, for example, did not suffer much — it was obvious that the chemists did important things, and the chemists deliberately emphasized their value in this way to make sure they didn't get wrapped up in ideology. Biology in the USSR, by contrast, couldn't deliver results for Soviet problems (like famines and crop failures), making them especially vulnerable to fast-talking charlatans who could promise fast action (like Lysenko). People who worked on modern physics appeared vulnerable in the 1920s-1930s, but the discovery of nuclear fission in particular gave them quite a bit of "insulation" against sustained political attacks on the content of their work.