There seem to be two, perhaps three, sources of mutation in WH40K - one, of course, is the "influence of Chaos" and the other is, curious enough, the exposure to entirely mundane environmental hazards - toxic waste, radiation, etc. - and the third, although it is perhaps only increased by the second, or is perhaps also caused by Chaos, is a natural proclivity of humanity towards mutation, though the creatures produced by these disparate factors usually all end up finding a home in the forces of Chaos. With regards to the "influence of Chaos", some mutations here are bestowed by the Chaos Gods themselves on a willing recipient (a Champion of Chaos). However, many instances of abberation did not require the direct intervention (though perhaps still were guided by the will) of a Chaos God. I fail to see a pattern in the immediate cause for such instances of mutation, though - merely being in the presence of creatures of Chaos seems insufficient, otherwise mutation would be rampant among those fighting against CSMs and daemons - one has to be in direct contact with the Warp in order to mutate. Then again, we see cultists sporting mutations without ever coming into contact with the Warp, and know only that they have religious affiliation to the Chaos Gods. The CSMs, too, began mutating only after they declared their affiliation to the Chaos Gods. Setting aside Dark Heresy, where mutation is a game mechanic consisting merely of the rolling of a dice by the GM and requires no consent whatsoever, can it be assumed that in order for Chaos to mutate a person, at least after birth, that person has to have consented to serving Chaos? Is there validity in seeing mutation as a "spiritual corruption"? And what determines the kind of mutation that one is subjected to? Is it in each case entirely determined by external factors, or does the mutant-to-be get a say in, or through some other attribute influences, the kind of mutation received?
Ad you mentioned yourself, not all mutations came from Chaos Gods (just as your sniffles are not necessary made by Nurgle). Mutants are somehow tolerated in the empire, although they are rarely treated much better than slaves or, at best third class citizens living in ghettos (although there are exceptions : Sanguinus by any standard was a mutant with huge angelic wings and he is now the most revered primarch).
When it comes to Chaos mutations - if you play with coal, you can get dirty. Of course there is much lower chance to get mutation by someone, who is actively trying to prevent them, by attending regular physical and spiritual cleansings (Imperial Guard fighting Chaos) or, by someone extremely strong willed (like Night Lords or Iron Warriors that are mostly untainted, even after long exposure to Warp), than by actual cultists, that welcome and even beg for such gifts. And even if they don't want them... Well they got it as a part of the deal.
Mentioned above Iron Warriors and Night Lords are example that you do can resist mutations: by general rule they are not worshippers of the Ruinous Powers, but instead they are trying to use Warp as a tool. While there are obviously cases of mutation among them (obliterator virus mutation is relatively high among IW), they are treated as effect of weak will of the mutated rather than gifts.
Exposure to to Chaos taint can cause mutations. Strong will and faith can prevent it.