This exact thing (with methane) has happened before and it is believed to be the cause of the extinction of extinctions, the PT event.
Yet we can tell they don't take it seriously, because they are adamantly opposed to nuclear power, which would defang coal, a major contributor to climate change.
One of the reasons otherwise reasonable people don't take AGW seriously is this kind of disconnect, in which the people who make the most noise about it are so clearly, obviously and transparently inconsistent between what they say they believe ("AGW runs a serious risk of creating civilization-ending events") and what they actually believe ("Global industrial capitalism is the root of all evil").
This is unfortunate, because AGW is a real problem, and should be addressed aggressively by both technological (nuclear, solar, etc) and political (carbon tax) means. But neither will happen until people start actually taking it seriously, instead of simply using it as a stick to beat some political hobby horse.
Denialists are little better, of course, but I honestly think it would be possible to get them mostly on side--and I have had some success in doing so--by sincere and consistent arguments that separate the science from the rabidly anti-capitalist, anti-industrial proposals for solution.
As to the methane issue, there are a number of scientists who think about it quite a bit -- and probably don't sleep much as a result. The problem is that two decades of intense lobbying and industry pressure have taught mainstream scientists to be incredibly conservative about their predictions. If the IPCC started including methane releases in their predictions, they'd be quickly torn to pieces for promoting speculative theories.
As for the nuclear stuff: if you're just looking for an excuse to not to care about climate change -- then go ahead and don't care about it! You're well aware that the main policy proposal on the table is a carbon tax of some sort and that such a policy would benefit both renewables and nuclear -- basically any technology that doesn't use the atmosphere as a waste dump.
It won't, methane doesn't "want" to mix with water anyway, at normal pressures and temperatures any dissolved methane will start to bubble out and float away.
> Can we filter it out?
It leaves on its own. Most of the time when you're concerned about methane in the water, it's because the water is being pumped up from underground where they were trapped together. The main risk there is explosions or fires if your equipment doesn't bleed off the methane safely.
> I imagine even if we could, other animals will still go extinct, which would disrupt our food chain.
Whoah, no, no no... you're thinking of something very different from methane, like perhaps heavy-metal contamination.
Methane isn't toxic unless there's a ridiculous amount pumped into a room. [Corrected: Odorless] Most animals generate some methane when digesting things.
TLDR: Nope, the issues with methane are going to be the climate and ozone-layer, not water-supplies.
Methane traps up to 100x more heat in the atmosphere than an equivalent amount of CO2 (over a 5 year period) and 72x more heat over a 20 year period
Source: http://www.onegreenplanet.org/animalsandnature/methane-vs-ca...
For drinking water aeration is probably sufficient to deal with methane content (but I don't think it's necessary very often).
Methane derivatives on the other-hand are known to be dangerous and can form as by products of disinfection http://en.wikipedia.org/wiki/Trihalomethane.