How long is one obligated to keep a kid’s gift?

I think we as a society need to be a bit less sensitive about gifts. I think it is fine to not like a gift. What matters is that they thought of you to get something. Sometimes it won't land. It is better to admit that (if necessary) than hide it forever. It isn't my responsibility to love and care for a give that you give me.

I get you something I don't want it wasting space in your house just because you are afraid I will be offended. That is like the worst outcome of a gift, I don't want to be giving you a burden.

So if the kid is no longer interested in the toy I think it is fine to give it away or otherwise get rid of it. If the person is offended they should chill the fuck out.

how long before you’re not offended to find out it’s been chucked?

If it's the kid's decision, personally, 0 seconds. Though, in that case, if it were just to be thrown away* I'd rather take it back and return it or resell it, perhaps even just for symbolic value so that it isn't wasted.
This is true for everyone. It's stupid to hoard useless gifts. But then again, I also consider gifts a bad idea all together.

*If the kid says he wants to sell it to someone, exchange it, gift it,... , that's reasonable.

If it's the parent's decision, infinite time, unless it is rightfully** ruled the gift was inappropriate ^(sorry).

**E.g.: "He's too old to have plushies." is not reasonable.

If you are offended by it being chucked, you didn't give a gift but an obligation.

It fucking depends. Kids lose and destroy shit constantly so if it's a plushie and the kid keeps it with them on road trips then randomly chucks it out the window... it's gone. Normal people understand that toys will all eventually be broken or lost and sometimes it happens surprisingly fast. If it's not really meant as a toy though (i.e. great grandma's doll from when she hid in an attic during the holocaust or similar sentimental value) never treat it as a toy - put it in a bank vault or storage locker until the kid is old enough to treat it delicately.

We always try to give stuff that can be used up. Art pads, scratch art, that sort of thing. So we expect things to not stay forever.

Of course we live in a tiny NY apartment and so do our kids friends, so that colors our choices.

It really depends on the gift recipient. Is the kid going to miss it?

The moment it is gifted it becomes their property, so whenever they have no more use for it. I am giving it away knowing that they may not find it amusing very soon or they break it because kids.

Whenever you or the kid chooses.

Wouldn't be the first time I've send an inappropriate or annoying toy to charity before my kids even had a chance to open the box.

It's nice if they take to it, but kids are fickle. I wouldn't be upset at all unless it was a toy that held sentimental value for me personally, and even then that's more of a me problem

I would be sad to see a kid not enjoy a gift and do that, but not outright against whatever they do with it.

It's a gift. If they don't like it I hope they find a good destination for it. Maybe somebody else will be happy with it.

I give it away, and then I don't really care anymore, unless the gift was expensive and specifically asked for.

I don't waste my time by being offended about things that I have no control over. I've added my positive contribution to the situation, do with it what you want.