At least some crematoria routinely emit pollution. When my brother died in the summer, in the Inland Empire of CA in the early 2000s, I was told that cremation caused a lot of emissions. It was very regulated because that area is often smoggy. We actually had to pay a surcharge for his cremation because he was a big guy and would pollute more.
My experience involves just one in Greenwood Cemetery in Brooklyn NY. When that thing is going there is no smoke, just INTENSE waves of heat. No particular smell either.