"no respect to religions" will be difficult practically to achieve in the initial phase, but the constitution will be guided by scientific socialism which will ensure that religion does not interfere badly in the social sphere.
for example, weddings should be done as court procedure with only two witnesses other than the bride and groom and the notary... no south asian wastage weddings... things like this.
and yes, no system subsidy or system support for pilgrimages, whether for hajj or for vatican or amarnath.
indeed, and especially so in case of india where secularism means "i will support your religious nonsense if you support my religious nonsense".