As they came personally to invite you go to their house with present and explain them inshallah they will understand
I was invited for my neighbor's wedding, which is on 15th and 16th of Muharram. I informed them I cannot attend till 2 months, yet they personally came to invite me. What should I do?
Convince them that i am a religious man and my religion is important than other things so that is why iA will not accept this invitation. If they dont accept it than you can go but appear like a mournful and show them that you are upset because of moharram and you should advertise the holy month of moharram and imam Husain a.s