I got a thread from the mosque which was kept on hazrat abbas alaam during Muharram. Now since I am wearing it I am married in a sunni family, I am being told to take it off as that is shirk and Islam does not permit this. Could you advise me on this please.

This is definitely not shirk. It’s seeking blessings of Allah through Hazrat Abbas’s loyalty and sincerity. Kindly explain to them Allah is the main source of blessings and thread is connected with someone who is highly blessed by Allah. Hence, you have it with you.
If they insist and you realize it’s causing fitna in the marriage, there is nothing wrong in removing it and put it either in your wallet, purse, hand bag, pocket etc