#1) The posters in no way assist in the location or rescuing of any hostages as the hostages are not in the USA or any where close to it. So there is no practical value to having their photos spread around. That means the posters are purely political in nature designed to elicit political sympathy for Israel.

#2) If the posters are put up without adequate permission which they usually are, they technically constitute vandalism in which case tearing them down is arguably cleaning up vandalism which is considered a public service. That's just the legal aspect of this.

So in the end, it doesn't help the hostages, and people have more right to tear the posters down than to put them up.

I would actually side with those tearing the posters down.

I probably would too, but I really hate kooky lefties.