Many restaurants in Israel, when asked about their kashrut status, reply that they are open on Shabbat. Thus, no hechsher. This also exists in establishments that would have a relatively easy time obtaining an hechser, like an ice-cream shop.
My question is, if the ingredients are kosher, is there any real issue with buying from them on a weekday? Besides marit ayin and interests in boycotting non-religious establishments, what makes the food itself forbidden?
I don't think treif ingredients is very common in Israel, at least from my experience. It's hard for me to imagine secret treif and meat mixtures in an Israeli ice creamery, for example. What I'm more concerned about is whether a seller's trustworthiness to tell the truth (jeopardized by selling and cooking on Shabbat) is the only issue here, or is there something else that makes the food not kosher.
Does the lack of a mashgiach affect the status of food? Does a kli used for cooking on Shabbat affect the food made on a weekday? Would indirect attainment of such food b'dieved (receiving a scoop as a gift) be forbidden?
Sources would be gleefully appreciated.