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Both propane and gas are sequestered carbon - its just a matter of how long you are willing to wait for them to form (ie. charcoal takes the lifetime of a tree and gas could take millennium)....
Therefore burning either is simply a matter of "returning carbon back to the atmosphere" -
but since the current problem is too much being released against a slower natural sequestration rate resulting in rising greenhouse gasses - both are environmentally negative (ie. not neutral)
Then when you consider the relative inefficiency of charcoal to gas burning, the huge expense of preparing and transporting charcoal vs gas and the huge amount of additional pollutants that charcoal produces vs. gas and you quickly realize that the enviromentalist should be gas grilling (or not grilling) - vegetables only - if you want to have any credibility.
But that being said - 99% of this stuff is pure nonsense anyway - if current models are to be believed - the difference of 10 yearly bbq of charcoal vs gas or a 25mpg SUV vs a 27mpg wagon wont make even the slightest difference.
You want to make a singular and meaningful difference? take mass transit to work everyday and live in an apartment (with scaled heating/AC) vs a private house. Everything else is mostly so small as to be meaningless