The rebuilding raised a constitutional question in the year it was finished, and the people arguing about it were the people who had just written the constitution.
The objection
Jawaharlal Nehru, prime minister, held that the government of a secular state had no business rebuilding a place of worship, and that the head of state attending the installation would compromise that principle. His objection was to the participation of the state, not to the temple.
The answer
The project had already been arranged so that it could survive exactly that objection. It was run by a trust and paid for largely by public subscription rather than from the treasury, which allowed its supporters to say that the state was not rebuilding anything.
Rajendra Prasad attended and performed the installation on 11 May 1951 in what was described as his personal capacity. The formula distinguished the man from the office, and it did so at a ceremony everyone present understood to be national.
Why it mattered then
India in 1951 was three years past partition and one year past a constitution that guaranteed freedom of religion without establishing one. What the state could and could not do at a religious site had no settled answer yet, and this was the first large test of it.
K. M. Munshi, who ran the project, argued that restoring a destroyed shrine was an act of national repair rather than of religious establishment. Nehru did not accept the distinction. The disagreement was aired and never resolved, and both men remained in the same cabinet.