The following piece will not dig deep into the concept of religious belief and how it may or may not be different than other sorts of belief or committments. I have done that elsewhere.
I am happy to live in a country that is fairly secularised in the political sense. This secularisation is of the sensibly liberal and tolerant kind, where people of openly displayed, institutionalised religious affiliation are as welcome as anybody else to run for political office, and anyone that may feel like it has the right to make religiously grounded arguments to support or reject political suggestions. Of course, it is also free for all to publicly display whatever symbol of one's faith on one's body that one may please – just as free as it is for anybody to display any sort of symbol of any kind, as long as these are not of particular types of political meaning (due to hate speech considerations). At the same time, while there are quite a few people in Sweden that belong to or identify with institutionalised religious organisations, rather few take the specific content of their faith into the realm of politics or public debate, albeit this content may inspire their political opinions and influence, e.g., voting behavior. These people expect, quite reasonably so, to be left free by society and other people to practice their religion as they please within then the same legal framework that demarcates acceptable behavior for any sort of personal or life-style activity. True, other people may have opinions about this and are free to express those, just as they may have opinions on any sort of activity of other people, but that's nothing special for institutionalised religion. In cases like this, which are the most common in my own country, people's religion are undoubtedly a purely personal matter, just as one choice of favourite sports team is.
Fine. But what about when a person of such religious commitment takes it with him or her into a political career, in particular when such a person belongs to a religious institution that openly propagate particular and strong political views, say, with regard to the legislation around abortion or people of LGBTQ sexuality. This is a heated issue at the moment in my country, as our prime minister, who represents a party (Moderaterna) presenting itself mainly as a liberal or even (when it comes to taxes, public services and trade) libertarian political body – although in the now rather distant past, it used to stand for a more traditional value conservative stance (King and Country and Church and the glorious days of old and so on) – choose to include in his newly formed cabinet a minister of just this sort of religious affiliation, Elisabeth Svantesson. The choice sparked immediate controversy (here, here), as Svantesson used to belong to an extreme neo-calvinist, Christian right, militant pro-life church, called Livets Ord, has been markedly active in the organised movement against current Swedish abortion legislation, and now belongs to a church called Kristet Centrum, that is not only openly oppose that legislation, but also openly stands for very negative views of LGBTQ people and seems to propagate a rather restrictive room for them to entertain the same rights in the area of family as others (Swedish links: here, here, here, here, here). A young, female representative of Moderaterna has publicly demanded that Svantesson officially distance herself from the political movements against legal abortion etc., or at least clarify where she stands. Svantesson herself has tried to rebut such requests as being about a "private matter", and she has been defended against the criticism by a number of debaters claiming that the critique is an example of persecution – the word "witch-hunt" has even been used – due to her religious faith, albeit one analyst has made the point that she is probably being let off the critical hook more easily than if she had been a muslim and had had a history of fundamentalist views coming from that particular camp.
My own view is the following. When a religious organisation propagates particular political views as part of its religious message, the question of whether or not a person of political office belongs to or sympathises with that institution or its message is certainly not a private or personal matter anymore. This is so, because such a religious institution is just as much a political organisation – the one does simply not exclude the other. The fact that such a political organisation also has a religious side to it cannot and should not immunise it against public critical scrutiny of the political views it represents, and the same goes for its political representatives. In this case, Elisabeth Svantesson.
The remaining issue is, of course, how sound the criticism is. With the extremely solid public support of the Swedish liberal abortion legislation (a pregnant woman a a positive right to have an abortion performed up to pregnancy week 18, after that it is very very difficult to have one and special permission is needed, but out of the question if the fetus is viable), the possible smuggling into the highest circles of political power a person committed to the opposite view would seem pretty relevant for voters. Similarly, a predominantly liberal/libertarian party lika Moderaterna, would seem to have a qualified identity problem if one of its highest political officers and most influential members represent ideas in the area of sexual orientation and identity related rights that sparks such a stark contrast to the party mainstream as reports suggest. True, with about a year to the next parliamentary elections, this is mostly a tactical problem for Moderaterna, but my point is simply that the fact that the problem has its roots in a minister's religious fundamentalist convictions does nothing to make it go away, in fact or even ideally. In conclusion, Svantesson needs to come clean and cannot hide behind a shield of alleged privacy or immunity against criticism for religion-based political ideas.