Any one who calls himself a Hindu should be accepted as a Hindu provided of course the person has no ulterior motive.
"I want to see you Swami", I began, "on this matter of receiving back
into Hinduism those who have been perverted from it. Is it your
opinion they should be received?
"Certainly", said the Swami (Vivekananda)," ...
Swami Vidyaranya (aka Madhavacharya) the 12th Jagadguru of Śringeri Śarada Pītham from 1380-1386 who is credited for founding the Vijayanagara empire, enumerates five conditions for someone to be considered a Hindu
गोभक्तो भारतगुरुर्हिन्दुर्हिंसनदूषकः |”
The above translates to that
He who 1) believes in “Omkar” ...