I guess I'm not sure what you mean by a heathen government. Do you have an example?
At this time, no, since Heathenry (with a capital H) is a new religion, less than a century old and almost entirely comprising of First Generation Heathens (that is to say, there aren't very many children being raised as Heathens.) I have to deal solely in hypotheticals, as a result.
For example:
Historically, Germanic-speaking tribes were generally divided into three social classes: Thralls, Churls, and Earls. Respectively, slaves/servants, "freemen", and nobles. While there was some theoretical movement between these three classes, considering the far-right tendencies of many Heathens, I would not be surprised if a Heathen government implemented this to behave more like the caste system of India.
As another exmaple, let's consider if a Heathen equivalent of Daesh showed up. I would expect a lot of their rhetoric to distort notions such as weregild and inhereted luck, to raid and destroy churches as "revenge" for some of the things some Christians did a thousand years ago (such as the Felling of Thor's Oak), and if they attained political power, might even outlaw Christianity and all Christian imagery and media. Which would be bad for me, because one of my most important Yule traditions is to watch the Patrick Stewart version of A Christmas Carol.
Yes I find this a bit disconcerting to say the least. US may not want to institute sharia law, one because of the constitution kinda being against that sort of thing but some Christians(some states even) would rather rewrite the constitution to allow something similar to let "God", or the bible rather, into the government.
As someone who is neither Christian nor Muslim, I see no significant difference in either.