I only recently became aware that this is apparently a topic of debate in vegan circles. Oysters and mussels lack a brain and central nervous system, and they are immobile. Thus unlikely to experience pain or any sort of sentience.
Being vegan for ethical reasons, I haven't really found any convincing arguments for why we shouldn't eat them (during my limited research so far). Most vegans seem to be against it. The two most common arguments I saw were "they could feel pain in a way we don't know about, so we should err on the side of caution" or simply "they're animals and vegans don't eat animals". The first one seems a bit too close to the classic "but what if plants have feelings" argument, and the second is just semantics.
I don't really see myself incorporating bivalves into my diet any time soon, since they weren't a part of my diet even before I went vegan, but I thought it was an interesting topic. What do you ladies think about it?
Some links: https://theanimalist.medium.com/on-the-consumption-of-bivalves-bdde8db6d4ba https://vegancalm.com/bivalvegan-diet/
When in doubt about the animal/plant itself, such as with oysters and mussels, it might be helpful to also check the way they are grown and harvested and whether that's harmful or not to animals and the environment. I have no idea about oysters and mussels myself, but it could be interesting to see if they are grown in wasteful water farms or if they are caught with nets or such that harm other animals and nature too.
I don't eat oysters and mussels, but I feel it's very easy to not eat them (at least where I live). They are an expensive and rare food and you have to go out of your way to buy and prepare them. Why bother when in doubt about their sentience or pain? I'd rather, like you mentioned, err on the side of caution and choose the easy path of consuming something else.