No beating around the bush, It was nothing to do with politics, there was no interest in putting secular in the preamble because they didn't see the need as also what I have stated earlier. However no one had doubts about the secular nature of the constitution and that was the view of the courts also.
The Indira Gandhi government through the 42nd amendment made a lot of changes, the preamble changes were minor compared to the others made. This was probably done as a sort of a cover since no one objected to the change in preamble but other changes were more crucial. Please read up if you wish to have additional information.