I'm sure there's a lot more to say on this subject but I would just like to take the opportunity to point you to /u/georgy_k_zhukov's fantastic post on the Czech Legion, which is one of the most interesting posts I've come across in this sub. I think he might have an expanded version of it somewhere as well but I'm struggling to find it.

There certainly was tension caused by the soldiers from opposing sides coming together after the war. Generally speaking, the postwar atmosphere saw the Czech Legions lionized, whereas those who remained to Austria-Hungary, particularly the officers, did not receive a warm welcome and in fact sometimes found themselves in a disadvantaged position.

Seeing as the vast majority of Czech soldiers involved in the war fought on the side of Austria-Hungary, you can already see how that might turn out to be a problem. Roughly 1.4 million Czechs are estimated to have fought in the Austro-Hungarian Army, and only about a hundred thousand would make up the Legions. These would not be all defectors from the Austrian army, mind you, but expatriates and the like as well. I wrote a bit about Czechs in the Austrian army some time ago in this thread in case you are interested.

After the war, the Legionnaires themselves as well as their legend would play an absolutely crucial role in the establishment of Czechoslovakia and its fledgling years. Their story, particularly in Russia, is undoubtedly fascinating – indeed, their fight and subsequent long voyage home is very often called Anabáze in Czech, Anabasis, after Xenophon's story of similarly stranded soldiers from ancient Greece. As those who actually fought against the monarchy, they became a key part in the founding myth, so to speak, of Czechoslovakia, and would come to wield major influence in the military.

On the other hand, the soldiers returning from service in the Austrian army were not seen in such a positive light. Perhaps rather understandably, as they stood for what was now being perceived as a repressive, decrepit empire that only stifled the attempts at autonomy or independence. They also had to undergo a sometimes lengthy demobilization process before going home or receiving new assigments – after all, Czechoslovakia required a military basically as soon as it was established, with several clashes with its neighbors and the need to secure its borders.

There was an ideological portion to the above, a so-called "odrakouštění", "de-austrianization" if you will, to transition the army from one loyal to the monarchy to one fighting for the newly independent country. Now this was a society-wide phenomenon – imagine school curriculums being amended, laws changed and so on – not limited to the army, where it was largely a matter of basic lectures on the fledgling democratic state and the like. However, the dislike of the former state of things was very real in the armed forces and manifested itself further, as Austrian medals were prohibited, the ministry of defense actively worked against veteran groups organizing events in remembrance of their former units of the Austrian army, or these soldiers being discriminated against when it came to pensions.

This also posed a new set of problems. The loyalist officers still comprised an educated cadre that could not be easily or immediately replaced in the Czechoslovak armed forces. In the first couple of years after the war, they would make up about a third of the officer corps. It would take some time before many of their remaining numbers were removed from important positions in the army in the 1920s. Not all of them, however, for example Jindřich Hanák, a colonel in the K.u.K. forces, would become a general in the Czechoslovak army.

It was not all just a matter of political inconvenience in the military either. A degree of antipathy against the officers and soldiers in question, as symbols of Habsburg rule, could be felt outside army circles as well. There were those who stood up for the majority that found itself on the defeated side, but they too would face criticism. One of the more notable examples is historian and writer Arne Novák whose conciliatory views were not well-received by pro-Legionnaire press.

I am afraid I cannot comment on what, if any, ethnic issues were exacerbated by this. I only know that after the war, the German speaking veteran organizations were forced to cut official ties with their Austrian or German counterparts and register in Czechoslovakia, and had to denounce their military traditions and loyalty to the monarchy. As for Czech soldiers, by the 1930s, there was a thaw in the tensions mentioned above, with veterans groups being established again – a fact that was quickly taken advantage of after the German occupation of the country and the establishment of the Protectorate of Bohemia and Moravia. The authorities saw them as Legionnaire-free and consisting of soldiers not entirely loyal to Czechoslovakia, and encouraged their existence. Unsurprisingly, after the second war came to an end, these collaborant organizations were disbanded and their leaders executed or jailed.