If I'm not mistaken those are just channels that the siding slips into. I don't think the spiders are going to get anywhere but inside the channel and that's not a big deal. However if you really have your mind set: I'd use an outdoor worthy caulking and get to work. You're going to have A LOT of caulking to do; under/at the end of/ each lap of siding.
Maybe if it's only spiders you're worried about you should get some sort of spray designed with them in mind?