As the question asks, if the USA would be justified to engage in civil war to for a state back into the union, as a lot of people I have asked in person have stated in their opinion, and Ukraine was recently integrated in Russia but declared independence and left, why isn't Russia justified in going to war to bring Ukraine back into union with Russia? As further qualification for a response to the question: bias against Russia or Communism is not good enough justification. It must be something else that we could also hold USA accountable to.
Setting aside moral arguments, let's just look at the relevant law. Texas vs. White established definitively that the US Constitution prohibits unilateral secession of states. In fact, the justices found that the Constitution bound the federal government to stop secession of states, since the constitution bound states to a "republican form of government" and gave the federal government the power to put down insurrections.
In contrast, the accords that laid the foundation for the Soviet Union were dissolved by the Belovezh Accords, signed by both Ukraine and Russia. Given that both Russia and Ukraine and their parliaments ratified the Belovezh Accords, it is abundantly clear that the Soviet Union and therefore the political bonds between Ukraine and Russia were dissolved in a legal fashion that leaves no possible legal claim for Russia on Ukraine.
Furthermore, although Russia was the pre-eminent republic of the USSR, it had no legal special status within the federation. The independence of Ukraine did not constitute secession from Russia, but a mutually agreed dissolution of the federal bonds between the legally co-equal republics of Ukraine and Russia.
Also, Ukraine is acknowledged as a sovereign state by all other countries, including Russia. One of the rights of sovereign states in international law is territorial integrity and in having diplomatic relations with Ukraine as a sovereign state, Russia is acknowledging that Ukraine has a right to territorial integrity, i.e., not to be invaded by other states.
Why shouldn't Russia do this? Because it should stand by its treaty commitments:
Budapest, 5 December 1994
The United States of America, the Russian Federation, and the United Kingdom of Great Britain and Northern Ireland, reaffirm their obligation to refrain from the threat or use of force against the territorial integrity or political independence of Ukraine, and that none of their weapons will ever be used against Ukraine except in selfdefense or otherwise in accordance with the Charter of the United Nations.
The United States of America, the Russian Federation, and the United Kingdom of Great Britain and Northern Ireland, reaffirm their commitment to Ukraine, in accordance with the principles of the CSCE Final Act, to refrain from economic coercion designed to subordinate to their own interest the exercise by Ukraine of the rights inherent in its sovereignty and thus to secure advantages of any kind.
Ukraine was recently integrated in Russia but declared independence and left,
That is false (unless your "recently" refers back to Kievan Rus').
It was the USSR that Ukraine was integrated in. So was Russia. The USSR has not been a thing for some decades how, so your statement is as much true as it is other way around.