There are many machlokes between different rabbis; some say that x is permitted and some say that it is forbidden. Jews believe that we are created ‘btzelem Elokim’ which means that we, like God, have to power to create, to change the natural order. That is why halacha is ‘not in heaven’ – it is on earth for the rabbis to decide.
By definition, someone who doesn’t hold with this is basically saying that when there is a machlokes, one rabbi is right and will go to heaven and the other who is wrong is sinning.
That ‘torah lo bashamayim’ and that rabbis have the power to affect the natural order via their halachic decisions is such a basic concept or orthodox judaism that I am shocked that you seem not to know it.
Therefore, when a gadol, who is reliable, states that x is kosher, then for all his followers, x IS kosher. End of story. And all other rabbis must accept that for those people x is kosher even if it wouldn’t be for their followers. Therefore those children will not have the spiritual definition of mamzerim.
I am shocked to think that people here actually thought that when there was machlokes through the ages it meant that one side was right and the other wrong, as opposed to both being right but using different concepts to arrive at different conclusions.