Let us for a moment one side or the other can make chlorine. They still need a lot of it. The first gas attack at Ypres used 150 TONS of chlorine! In addition to the gas, you need to include the weight of the cylinders in which it was carried (and making lots of cylinders capable of holding chlorine under significant pressure is beyond the capability of the CSA). Let's say that makes the total load to be transported from the nearest rail head to the battlefield 200 tons. Let's say only about 1/3 of this amount has to be used, that' still about 75 tons that has to be transported from the nearest rail head - certainly doable but not trivial. OTL it took the Germans some time to set up the cylinders for the attack, and then they had to wait for the wind to be in the right direction.
Most of the CW battles, until the latter part of the war at Petersburg for example, were not long term sieges with fixed lines but more like Gettysburg, Shiloh, Antietam, etc where the armies came together for a relatively short period of a few days at the most and then moved on either in advance or retreat. These are not conditions where you can do the sort of Ypres gas attack. CW era artillery was almost always direct fire, which does not work with gas shells even if you can make them. On top of this weather forecasting during the CW era was limited at best, so you could only attack with gas if the wind was right at that moment, and hope it did not shift. Finally, if your troops are going to take advantage of a gas attack, they have to be equipped to operate in a contaminated environment - if not when the gas dissipates the enemy retakes the abandoned positions.
Neither side in the ACW had the industrial capacity to make the required amounts of chlorine and the pressure tanks to deploy it, even if small amounts of gas or a few tanks could be made. Long range indirect fire which is needed for gas attacks by artillery did not exist to any extent. Once off the rail net, transporting large numbers of gas cylinders becomes a significant logistical burden over bad roads with animal drawn wagons. Developing, and producing in the needed numbers, of adequate gas masks is absolutely beyond the capability of the CSA, as far as the Union goes maybe but the technology has not been invented yet. As opposed to the fixed battlelines of WWI with trench warfare, the vast majority of ACW battles large and small were battles of moving armies. The exceptions like Vicksburg, occurred where the CS forces had no access to the supply lines that would allow them to get enough gas to matter, or Petersburg, occurred too late in the war when the CSA had lost much of its limited industry and the rail net was shattered.
Even if the use of gas was considered morally acceptable, certainly the south and most likely the north, simply did not have the capacity to do it.