Question: Is it sinful to be naked when one is alone at home or while one is taking a bath?
Yes, it is sinful because we are not alone. There are angels with us who protect us against genies and devils and who record our deeds with instruments like cameras. It is stated in hadith-i sharifs:
(A person must feel shy from the two angels with him day and night as he feels shy from his two pious neighbors.) [Bayhaqi]
(Refrain from remaining naked. Feel shy from and respect the angels of Haphaza who are always with you except when you are having sexual intercourse and when you are in the toilet.) [Tirmidhi]
(Do not uncover your awrah even when you are alone because there are angels with you who never go away from you. Feel shy from them and respect them.) [Ashiat-ul-lama'at]
(Refrain from uncovering your awrah when you are taking a ghusl at night. If a person does not refrain from it and then a sign of insanity develops in him, let him not blame anyone but himself.) [Hakim]
We are always in the presence of Allahu ta'ala, but the case is different as for salat. We should make ourselves presentable before standing in the presence of Him for salat. Allahu ta'ala does not judge us or our salats by our new and excellent clothes, but judges us by our hearts and intentions. He rewards or punishes us according to our intentions in our deeds. In spite of this fact, He orders us to wear proper clothes and to cover our private parts purely and simply for ourselves.
Allahu ta'ala of course sees us both when we are in salat and when we are outside of salat. Therefore, we should avoid being rebellious against Him and from displaying immodest behavior. It is stated in hadith-i sharifs:
(Allahu ta'ala likes bashfulness and one's covering oneself. Then cover your awrah when you are taking a bath.) [Abu Dawud]
(One's sense of shame from Allahu ta'ala is much more necessary than one's sense of shame from people is.) [Tirmidhi, Nasai]
(Cover yourself while you are taking a bath. Allahu ta'ala is the owner of haya [modesty, bashfulness]. He loves him who covers himself out of bashfulness.) [Nasai]
(Cover your awrah. Feel shame from Allahu ta'ala even when you are alone.) [Tirmidhi]