Intentions and Deeds
One example would be someone who puts on tefillin everyday, but in reality, the tefillin is not kosher. I want to treat this from a purely theological perspective, so lets say for the sake of argument that the person never finds out and it is purely a matter of God's judgement.
The opposite case - of someone performing kosher actions or using kosher ritual objects but for theologically heretical purposes - the rabbis rule their actions completely void of any theological value. For example, Rabbi Faur (in a fascinating article which I hopefully will be writing about soon) talks about the rabbinical position towards minim.
The law stipulates that a Scroll of the Torah written by minim – probably Judeo-Christians – ought to be incinerated together “with the names of God it contains (because even the Tetragrammaton, representing the holy of holiest, is contaminated with their idolatrous schemes). Addressing this law, they cited the verse: “and behind the entrance at the door-post (mezuza) you (i.e., the minim) have placed: your remembrance” (i.e., your idolatrous
schemes) (Is. 57:8). Meaning, they are using the mezuza – a sacred Jewish object – to package inside it their idolatrous doctrines! To put this less ponderously: appearances may be deceiving! The manifest reliance of the minim on the Torah and their use of Jewish values are a ploy intended to deceive and corrupt the dull-witted.
I was thinking of this in conjunction with the idea of a more heterogeneous Jewish society, such as advocated by evanstonjew. In this society one issue would be how much could the Orthodox trust the less than Orthodox in terms of intermingling with them, for fear of un-knowingly transgressing some halacha. If the real issue is intent, then the intermingling is more likely. For example, the Orthodox family inadvertently broke halacha, perhaps by being served food that was not kosher by a Reform family because the Reform people , while well intentioned did something against halacha while serving the food. However, if the real issue is deed, then the Orthodox family would need to take all precautions to make sure that they do not accidentally ingest any non-kosher food, thereby making the mixing of orthodox and non-orthodox truly problematic...