As per this thread, there are various opinions of whether the idol at the temple should be touched or not: Is it allowed to hug/touch the main idol at a temple?
Now there is a special case of Shiva, which is known as "formless" (Nirguna/NirAkAra) aspect of Brahman, hence it may not have any idol as such. Yet, it's primarily worshiped in form of "Linga" (Phallus/Penis): Why is Shiva primarily worshipped in a linga form?
Many years back, our history professor told that, Not everyone should "touch" or "caress" the Shiva Linga. Especially women shouldn't do that, for the sake of modesty.
But in case of God, shouldn't everyone have equal rights, especially in today's era!
Who are allowed to touch/caress, the "Shiva Linga" while worshiping?