I tend to get possessive at the sight of someone touching what's mine

am I rude by being like this?

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MrAverage1965 · 61-69, M

It depends what they are touching and how they are treating it.
My two most treasured possessions are an MP3 player my kids bought me and my noise cancelling headphones.
I would let someone else use them but only someone I knew and who would take care of them.