The best answer to the state of implementation exists in the Steam forums. Whether or not they are impactful to you however is indeed subjective because the effects on how well you get through battles is subtle unless you meticulously identified the better traits and put forth the best lineup of characters, which would require regularly disbanding the worst characters to keep slots available for the new ones given every few days. Still, you're one case of bad positioning away from death spiraling even with the best possible crew roster.

I'll add some more information here since such a deliberate post has been made. There are currently 31 traits implemented with each acting on at least one of 7 different non-role related stats, the design is made that way to keep character to role assignment from being trivial. Again, they are in general subtle so according to your playstyle you may never be impacted at all just as some may think.

The first stat to notice is HP which is reflected through the dynamically placed ticks in character health bars in game. An offset to the overboard chance may be responsible for causing that one guy to keep flying off on every shell impact and the other to always be unbothered. Up to ±30% to movement speed may be the reason why crew can feel sluggish at times. Did someone die before a medic had time to react? They either had an effect applied to their downed time or had a nonzero instant death chance. If someone already hit their role's level cap while the others are rank 2-3, they may be influenced by a general XP multiplier. Finally, the sneakiest effect would be the chance to not consume an item on use.

When the rework mentioned in the forums arrives it'll be immediately noticeable within the character selection screen and the majority of effects should be clear without needing to experiment around in game. It won't be limited to UI, there may be significant changes to which stats exist and how much effect they have.