It is permitted to eat on the utensils of someone who holds of an opinion regarding kashrut than you don't follow unless you know that they were used within 24 hours for the food that is problematic. The reason is because we assume that generally a pot wasn't used within the last 24 hours and as such the food made in those pots is fully kosher. The owner doesn't have to kosher his pots since according to the opinions he follows it is kosher and doesn't need koshering.
Serving Something that Someone Else Holds is Forbidden
If someone holds that something is forbidden and you hold it is permitted it is forbidden to serve it to him without alerting him about it because of the concept of putting a stumbling block before a blind person - לפני עוור.
If someone doesn't trust a certain hashgacha and you know for sure that it is a good hashgacha one can serve it to him without telling him. If he asks you directly you can't lie.
↑Vayitzev Avraham 2:47:5 writes that according to the Maharalbach it is only considered a problem of lifnei iver to trip him up on something that he holds is forbidden for a halachic reason. Each opinion can be authentic in a torah sense because of elu v'elu. However, if he has a mistaken opinion not based on a particular opinion or chumra then you can give it to him without telling him and it isn't lifnei iver since there's nothing wrong with it. Therefore if you know for certain that something has a good hashgacha and he is just concerned because of a rumor then you can give it to him without telling him. Lying if asked is a problem of genivat daat.