The Tosafot wrote that the concept of 'dina de-malchuta dina' applies exclusively to non-Jewish Kings; since the land is his and he can say that if one doesn't obey his command, he will expel them from the land; however, Jewish kings may not because all Jews are partners in the Land of IsraelTosafot are predicating 'dina de-malchuta dina' on the presumption that kings actually, in some way, own their kingdoms. The approach seems to be akin to the common sense 'As long as you in MY house, you play by MY rules' theory. Israel is the exception, because, since every Jew is a partner in it, no one partner may tell an ostensibly equal partner to get out.
Thus, many understand that the Ran would deny the validity of the laws of the modern State of Israel to the extent that they don't corroborate the laws of the Torah. It also opens the door for all kinds of abuses of the system for anyone who is 'kim lei' like the Ran.
However, I'd pose another question to the opinion of the Ran. How would he relate to a democracy in general? On one hand, it's similar to the latter case in that it's acknowledged that every person has an equal stake in the government under the 'one-man, one-vote' system. Or, in the words of the famous paytan 'this land is your land; this land is my land'. Ostensibly, then, no person has greater rights than any other, and then 'dina de-malchuta dina' would not apply in any democratic state.
However, specifically in a democracy one might argue the exact opposite. In the monarchy that Tosafot describe, the power of the king, manifest by the right/ability (big nafka mina in how to translate the word yakhol; I think it's closer to 'right') to deport untolerated segments of the population, means that no others have the true, inalienable right of residence. The King's will can always supersede the will of his subjects. Modern democracies, however, were framed so that each citizens has the inalienable right of residence ('property' in Locke's formulation) , and where citizenship implies that one can return to and not be deported from his homeland. Thus, in a modern democracy, every citizen is 'king'. However, citizenship also implies that one has agreed to abide the law of the country or its constitution. Each of the many 'kings' casts his ballot, or has the right to, as his say in how the country runs. It's his little slice of the 'monarchy'. Thus, the aggregate of 'the people - the demos takes on the role of the 'king', which each individual has contracted to abide. Failure to recognize the law can constitute either a renunciation of citizenship or a forfeit of the rights - such as freedom, or in extreme cases, life - that citizenship entails. Thus, even though all citizens are 'equal partners', 'dina de-malchuta dina' can still apply (though it would sound more like the formulation of the Rashbam in Bava Batra; Tosafot might agree with the Rashbam in a non- or constitutional-monarchy).
Thus, in the modern State of Israel, which is democratic and which extends the right of immediate citizenship to all Jews everywhere, the law of the land in no way undermines the 'partnership' of each individual. The Ran is essentially saying that Jews have an inalienable right to domicile in the Land of Israel, a right which the modern State of Israel upholds. Therefore, as long as the constituted Israeli democracy respects the rights of its citizens - even if some of its laws are non-halakhic, as long as every Jew is invited to participate in the decision process - the law of the land is, in fact, the law. However, if the rights of certain individuals are abrogated because of a non-universal rule - i.e., a particular segment of the population is singled out for unfair treatment, then members of that segment need not abide by the principle of 'dina de-malchuta dina' (a point which echoes R' Tam as quoted by the Beit Yosef in Ch"M 369, which would make the position of 'Tosafot' consistent in this matter).