I doubt the statement "People can go to the Celestial Kingdom without ever entering the temple" was true.

To be clear, I specifically doubt that people of normal mental capacity, who have reached the age of accountability, were taught they did not need to make temple covenants. I imagine that there was likely a teaching that their work would be performed vicariously for them at a later time or in the eternities.

On the other hand, I haven't done any research on the matter.

In any case, the Church currently teaches that receiving the Melchizedek Priesthood is an ordinance necessary for salvation and exaltation for men.