Does Islam support Muslims, in a secular country, to go against their government if the government does not allow Muslim refugees (Not for religion reason but for some bureaucratic reasons)?
On the authority of Abu Sa`eed al-Khudree (may Allah be pleased with him) who said:
I heard the Messenger of Allah (pbuh) say, “Whosoever of you sees an evil, let him change it with his hand; and if he is not able to do so, then [let him change it] with his tongue; and if he is not able to do so, then with his heart — and that is the weakest of faith.” (Hadith 34).
As a citizen of a democratic secular state there are allowed avenues of protest - voting out a government, writing to senators, MPs, charities or NGOs, or going on rallies, public meetings and marches - so these are protests of the 'tongue'; citizens who feel more strongly can engage in civil disobedience, and these are generally outside of the law and hence judged by the courts - so these are protests of the 'hand'.
Take for example the history of the Dakota Access Pipeline Protests as a very recent example where one can say all three possibilities were explored: by hand, by tongue & by heart.
Absolutely Not, they can influence the policymaker or authority by writing, peaceful demonstration and be participating in election etc. Muslims are also not allowed to go against a Muslim state or just rulers
I'm not sure how you define "war" on your question. But there a sahih hadith told by Tirmidzi, that moslem can criticize the despotic, tyrant or zalim goverment in a country.
إِنَّ مِنْ أَعْظَمِ الْجِهَادِ كَلِمَةُ عَدْلٍ عِنْدَ سُلْطَانٍ جَائِر
This hadith has a shaih (hasan) grade. You can look it up from https://sunnah.com/tirmidhi/33/17