No, I don't think there is any particular active attempt at suppression of this particular idea. Clearly some religions accept reincarnation while others don't, but that has long been the case.
There is a broader issue in the West, where there are intertwining threads of a broadly Christian history together with more recent science. The latter, science historically arose from those with various religious, spiritual or occult beliefs. For example Newton, known for his ideas on gravity as well as laws of motion, also was deeply invested in alchemy, a somewhat mystical area. Many other founding figures of science had either religious or spiritual beliefs.
But at some point there arose a view that science and materialist atheism were supposed to go together. One consequence has been that even consciousness itself is rejected as just an illusion or an artefact of brain processes. Some go further and claim that brain processes themselves are wholly deterministic and thus we are just machines. A lot of this is sheer bunk of course, yet it has acquired a foothold in supposedly respected institutions.
I tend to the view that there has been a lot of irrationality and muddle-headed thinking in some areas of modern thought. For a while I think there was an expectation that with a greater knowledge of the sub-atomic particles which make up our physical world, sooner or later everything would be understood and explainable by science. It was an unrealistic expectation, consciousness remains as elusive as ever. I think nowadays the idea that consciousness is fundamental, rather than derived from matter, is becoming more accepted. It seems such a small step, but on the nature and reality of consciousness, much else depends, including the possibility of survival beyond death and indeed before birth.
