As far as my PERSONAL (is that the word? ... perhaps "household" religious "guests" and paraphenalia) murtis, "God" posters, items from India such as sacred rocks, dirt, dust, small chips from ancient temples (not kidding), and so on, most of mine are in good condition including posters I have had for 45 years now. So I rarely have a situation where such a religious item has had to be "put in samadhi" if you will.
But in one example, even though some may object, I had a badly water damaged poster (small size) that I performed a funeral pyre then put the ashes in a local river.
I du not recall any Murti I have "disposed" other than the clay Ganeshas I make for holidays for immersion. Our house actually has a large "collection" and 90% are metal and many are valuable. When I die, before dead I will try to give these to the right people - for example if my daughter gets married I give to her children. A couple of these have powers inside them that might be dangerous in the wrong hands.
As for things such as cards with Deity on them, I have these in a box. I don't think I have ever thrown any out. Now that I think about it, too many, I don't know what will happen to them after death. I guess I don't get too worried about it.
The most important "thing" I have is a small chip of stone from the left side of the Bankibihari Temple Vrindavan India, and I have my personal silver Hanumanji Murti from the Delhi region but of very unique Adorn and Form of Brahmacharya with cap and rudraksha head band and arms/hands in almost "Muslim style" with prayer hands palm up, standing but tail at rest. This Murti has powers and is never to be discarded and must be passed on to generations.
No one is allowed to see my Hanuman other than those I allow. I know Rama doesn't like that idea, that is fine I will suffer the karma, but this Hanumanji has powers and I do not care if I am being selfish or protective even if I go to Yamaraj to explain.
I would suggest however, one can take these things too far. If someone chooses to politely dispose of old cards or posters and such, I do not have a problem. Nor do I tell others what to do.
Nor do I have a problem with taxis having Hanuman picture on the dash, or Sikh symbol painted on truck and things like that. In fact, I like it.
I do not mind Devatas or Devi being used as a product symbol, even if for things like soap. Sometimes people get worked up over things, not me, for example isn't Devi also in the Earth Herself? So if I sell dirt and my company symbol is Sita, what is the problem? She was born in fallow dirt dropped from a deer. So? She is Bhumi.
Now if someone goes to a temple and breaks the religious things, that I do indeed have a problem.
But, though this may be shocking to some Hindus to say, not every murti is actually an Idol. No. Some of those clay one's, or wood, or even metal, are nothing but clay or nothing but a decoration.. Not Idol. They are "empty". Not God. Just toss them if you like. They are not "awake". If you show me, I can tell you in 10 seconds.