Wasn't the cause of not going to war with Syria back in '13 because of the possiblity of a confrontation with the Russians?
They weren't present in the same way they are now. As OP said, one of the main reasons for the lack of a strike was that there as very little public or political support for such an action. Besides, I highly doubt we actually would have gone to war over Ghouta. It probably would have been similar to our actions after Khan Sheikhoun and Douma, limited TLAM and airstrikes meant to degrade Syrian chemical weapons capabilities. Perhaps we might have stepped up aid to Syrian rebels, and in an extreme situation we may have even had a Libya-style no-fly zone, but I doubt the latter - the collapse of Libya after Gaddhafi was toppled was a big reason why Obama and other NATO leaders were reluctant to intervene in Syria afterwards.
In any case, without the Iraq war there might have never
been a civil war in Syria to intervene over in the first place. The fall of Saddam and the subsequent occupation and insurgency had
major effects on the region, and are commonly identified among the root causes of the Arab Spring and the wave of radical Sunni terrorism that currently plagues the region.