This is a mind-bending question and I'm aware of the prohibition of giving advice that would encourage someone to violate halacha-but here's my reality. I'm a Jew and I have a kosher home. I am not shomer Shabbos but I have lived in a family and kept a shomer Shabbos life in the past primarily out of love and respect for my family and raised my step children in a Hasidish tradition. My personal beliefs don't require me to eat kosher something back then I would never have done in front of my children. But today I'm no longer married, my children are Hasidish but completely respectful of my beliefs as I am of theirs. It's of paramount importance that I have a home where my children, or any Jew at all, would be able to eat. I'm knowledgeable about the Halacha of kashrus and in my home, am as fastidious about maintaining kashrus under Halacha. So to the degree the answer might depend on whether a person who purchases an item on Shabbos knows that they are doing "wrong" it's not my belief that I'm doing "wrong" though I'm very aware that it violates halachica. I would never cook in my home on the Shabbos, for example. But if I bought a food item on Shabbos and cooked it in a kosher pot, considering my personal belief that it is not "wrong?" Would that food make the pot unkosher because it was bought on Shabbos?
I am not trying to be cute or avoid complying with Halacha, quite the country. So where a Bet Din, under the Halacha of Dina DeMalchuta Dina, is required to apply domestic civil law to certain types of disputes rather than in theoretical Halachic law, I think that it may be Halachically proper for me to do as I understand as I don't believe I am committing a "wrong" and don't believe in the Halachic obligations as a traditional believer does. I need to add a bit more context. I've been a lawyer for 35 years. I have little doubt that the reason I became a lawyer is because of my Jewish upbringing which is so centered around the importance of having a system of law that provides justice. I attended a law school that is part of a Jewish university. I am a civil rights lawyer and feel that my fighting for the rights of people who have been wronged is very much an expression of my Jewishness. I also represented observant Jews in civil matters where the Belt Din has granted them the right to bring that case where the respondent refused the jurisdiction of the Beit Din. I also doubt that I could represent an observant Jew in a civil court case where they knowingly were avoiding the proper jurisdiction of the Beit Din because I could not represent someone who was knowingly disrespecting our system of justice which has existed to serve and protect us since time of the Second Temple.
I know this will sound strange but I don't want to disrespect Halacha by following Halacha for reasons which--for me--would be hypocritical. Though I pose what I view as a complex question, my purpose in this question is simple in that I do not want to do anything that would effectively make my pots, plates etc unkosher because I purchased otherwise kosher food on the Sabbath. If doing so, within the context of the Dina DeMalchuta Dina legal system I where to, would tender my kitchen unkosher, snake to invite an observant Jew to eat it my home Halachically, I certainly will not do this.
I know this is a Halachic nightmare and I mean no disrespect to the sincerely held beliefs of any reader by asking this question on a site like this. To be clear, I'm not suggesting anyone to disobey a halaha which they know and believe they are obligated to follow. I have taught in a yeshiva, I've taught Torah outside a Yeshiva also blending traditional and social science perspectives and told together in the same class. I continue to learn Torah. Being Jewish and learning Torah is very central to who I am and my neshama and my connection to the ein sof as I personally understand that spiritual concept. But I also view myself as a modern scientific thinker. I very much view our civilization and our laws also from an outside perspective with social science tools. I know this is a conundrum but I feel it would be hypocritical for me to act based on beliefs I don't personally hold. Here I hold the belief in Who we are and that I am personally, spiritually and humanistically, but not risk religiously, compelled to keep a home that any Jew in the world can have dinner at. This is sometimes a painful and challenging place for me to live emotionally and I can guess you will tell me to consult my rabbi -- but as you can see this is essentially a purely objective halachic question that requires a halachically objective answer--if one can exist based on the framework of this question. Thank you so very much.