If a person converts in order to marry a secular, non-observant Jew is this conversion valid? I know that in theory the whole point of converting in the first place is to accept the authority of the Torah and live as a Jew. However in practice, as I’m sure you’re aware, most conversions are pre-cursors to weddings that would otherwise be intermarriages and have little bearing on the post-conversion habits of the convert. On one hand, it seems that this would not really be a valid conversion (and I know in Israel conversions can be denied in situations where the convert isn’t actually living a Jewish life). OTOH, we aren’t allowed to judge "born" Jews on what mitzvot they do or don’t do, are converts subject to a different standard?
Conversion requires acceptance of the Torah's truth and authority. A child born to a Jewish mother remains Jewish whatever his beliefs. A valid conversion requires a recognized Orthodox Beit Din. If such a Beit Din converted someone you should assume that all the relevant questions were asked and that the person converted to Judaism by that Beit Din passed the requirements.