People will vote on this according to what they believe but not on the evidence.
CO2 is the lowest energy gas. It cannot be broken down. It can only be removed by either chemical interaction with rock or by photosynthesis. Thereby once produced it will remain in the atmosphere unless we can increase one of these two mechanisms.
Methane is a high energy material. It is broken down quickly by sunlight, bacteria, ozone, lightning, dusts and other materials.
So that if we produced a huge amount of Methane today then stopped, in a few years it would all be gone.
The result is that the claims of dangers of methane are based on the wrong criterion.
If the atmosphere was full of methane ( like venus?) it would be a serious greenhouse gas.
However that is not a genuine possibility. It is a "red herring" accepted by one side because it diverts attention from the real issues and by the other because it is another tool to gain power by the "trump card syndrome".
This means if we increase our production of CO2 AT ALL without increasing the photosynthesis then the CO2 levels will rise and keep rising indefinitely.
If we increase our total methane production, from all sources both natural and human, by 5% then the concentration of methane in the atmosphere asymptotes to 5% greater. That makes it not a substantial problem.