It is very easy in India to blame anything and everything on Hindutva. While it is really sad that there is no proper management in the holiest Shrine, efforts hould be towards getting that right than blame on somethings else.
This is not an exception in India. Many Hindu shrines has got non-hindu persons as Executive Officers. In some holy shrines of Hindu, Govt even encouraged preachings of other religion
As of now we have enough tension between religions, castes, faiths, sects etc. Don't create another one for cheap publicity. If you are concerned with a sad plight of the shrine just talk about that - not some pre-conceived notions that are your own.