Our only obligation is to approach government in a way guided by the rules, principles, values, and objectives of the religion. And we can do that regardless of what system of government exists.
Look, we know that Rasulullah ﷺ said that shortly after his death we would begin to see things from the government that we didn’t recognise as legitimate, but that we were still supposed to regard those governments as legitimate and deserving of our obedience and loyalty. We were forbidden from revolting against governments that did not fully replicate the models of the first four Khalifahs; we were not ordered to overthrow those governments in order to re-establish the earlier models.
That is sort of the core lie of modern Islamism; certainly the core lie of Jihadism and extremist groups like ISIS who claim that it is obligatory to re-establish the Khilafah along the lines of the earliest forms of government in Islam. The reality is, no, we’re not. There is nothing whatsoever to support that argument.
Even the word “Khilafah” when used by Rasulullah ﷺ does not refer to a particular system of government; it just refers to whatever system of authority follows his death, it just refers to the successive systems of government that develop as time goes on. Rasulullah ﷺ used the word according to its linguistic meaning, not as a term denoting a specific model of government. Any specific model or structure of government that you may think is what Khilafah means, is a human construction, and by definition, not obligatory for us to adopt or impose.