Christian churches and Mosques may keep their doors open for people of all religion. It is not because of the catholicity of these religions. Basically they are prosylitising religions. They have a history of playing all tricks available to swell their numbers. Budget for the next harvest of conversion, as Gandhi wrote in Harijan long back.
The Organised church and Mosques are conducting themselves more like amultinational corporations doing aggressive selling of their branded products. Selling of Jesus and Prophet Mohammed (PBUH) is their sole aim and for this they have to definitely keep the door open.
Whereas Hindu way of living (not religion) is not a prosylitising religion. Therefore it has no compulsion to keep its door open for all and sundry. But temples have to open its doors for the Hindu believers no doubt.