Not sure where you're from, but at least for American-made wines that's not often the case, as there are many more common and/or cheaper sources for chitin, casein, gelatin, etc. (pig and cow, as well as egg based sources for example). Also, blood-based fining agents have been outlawed in the US and Europe since the mid 90s thanks to the mad-cow scare.

Of course this conversation also ignores the fact that fining agents are removed from wine before bottling as part of their purpose - they bind with the crap you don't want in your wine. Typical store-bought wine will have no detectable amount of a fining agent in it.