السلام عليكم ورحمة الله وبركاته شيخنا أحسن الله إليكم Is it permissible to buy items that may contain logos or symbols of kufr or shirk, and to use the product while disregarding the packaging and throwing it away after use? جزاك الله خيرًا

This is a very general question, and it could be anything that is kufr. Since you did not specify, the answer is: stay away from things that have disbelief symbols. This answer is for someone who does not suffer from waswas and OCD, because such a person might be looking into things too much and digging too deep. Otherwise, he could have bought them and not even noticed—that is, if it is actually kufr and shirk.