I just saw an interesting discussion about whether you can trust the kashrut of someone who has not kept other Torah commandments. Here are some interesting questions - I don't think there are any easy answers to these.
For the purpose of these questions, "eat in their house" means that you would be confident in going over to their home and eating whatever was served from their kitchen. This means you are confident that (1) they have knowledge of the laws of kashrut, (2) that they observe the laws of kashrut, and (3) that they are not going to purposely feed you something unkosher for nasty reasons.
Would you eat in the house of someone who:
1. Lives an Orthodox lifestyle, but is openly a criminal, such as embezzling money? (Referring to crimes that are not only against secular law but also halacha)
2. Is openly gay, but keeps a kosher home? (We actually know someone who this would apply to.)
3. Does not keep kosher at all, but puts in the effort to learn about what you would require in order to eat there? I have a cousin who bought me new dishes and cookware, and learned the basics of (non-meat) kosher food requirements, so that I could visit her.
4. Is a close friend of yours who used to be religious and became extremely anti-religious? This person would have the knowledge of how to prepare kosher food for you, but would you be able to trust that they wouldn't purposely serve you something not kosher?
5. Lives an Orthodox lifestyle but says nasty things about other groups of Jews non-stop during the meal?
6. Keeps chumras that serve to prevent them from eating at almost anyone else's house, and feels they are "on a higher level" than anyone who doesn't keep these chumras? (chumras=customs not required by Jewish law, that are more strict than the already-extensive laws that we do follow.)
7. Lives an Orthodox lifestyle but didn't have any formal halachic learning, follows most laws because "someone told them to", and therefore may not actually know the details of kashrut?
8. Lives an Orthodox lifestyle but is a bad cook? =-)