Mathura or Ayodhya is not the concern, its about Sikhism's link to Tamil vaisnavism , btw as a " Hindu scholar' I would have expected a more knowledgeable response, as Ayodya is the centre of the Ramanandi sect
When comparing the progression of the Bhakti cults in both North and South India, there is another important perspective to consider. This one is particularly emphasized by today's Sikh scholars. The home of Sikhism is the Punjab, in northwestern India.
There, a branch of kshatriya Vaishnavas developed their own unique religion, identifying with certain aspects of the Tamil Bhakti movement. This is describe by the Sikh author, M.S. Ahluwalia in his paper, The Bhakti Movement in Tamil Nadu and Punjab.
http://www.harekrsna.com/sun/features/03-12/features2388.htm
the word Hindu is Persian in origin, where is the mention of such a religion in your scriptures ?