What one must understand is that deodorants are mostly antiperspirants, and they are antiperspirants by being waterproof. The main way that our deodorants are waterproof is via an aluminum based-compound, such as aluminum zirconium tricholorohydrex gly(cine) among others. When you combine sweat, bacteria, sebum, dead skin, a waterproofing gel/solid, and absorbent cotton shirts... what do you think is going to happen!? Of course it's going to leave residue.
What would seem to be the solution is to stop using deodorants with waterproofing compounds, be they aluminum-based, natural wax-based, or including any sorts of oils. But keep in mind that what you're left with won't do that great of a job, definitely won't prevent pit stains, and may still leave you with discolorations on your undershirts--this time of a more yellowy kind from your sweat, sebum, etc, and the bacteria growing under your arms.
Personally, I use Mitchum unscented, which has the strongest concentration of the aluminum compounds on the market and has almost no scent (what is there is pleasantly boring and does not clash with any cologne or bodyscent in my experience)... and I wear white undershirts that I replace every year or so. If build-up gets bad, I bleach 'em with hot water and let them soak for a while.
What would seem to be the solution is to stop using deodorants with waterproofing compounds, be they aluminum-based, natural wax-based, or including any sorts of oils. But keep in mind that what you're left with won't do that great of a job, definitely won't prevent pit stains, and may still leave you with discolorations on your undershirts--this time of a more yellowy kind from your sweat, sebum, etc, and the bacteria growing under your arms.
Personally, I use Mitchum unscented, which has the strongest concentration of the aluminum compounds on the market and has almost no scent (what is there is pleasantly boring and does not clash with any cologne or bodyscent in my experience)... and I wear white undershirts that I replace every year or so. If build-up gets bad, I bleach 'em with hot water and let them soak for a while.