I understand the "why" of doing this is controversial, and everyone has differing opinions, are all worth considering. OP asked what options are, not if it is the highest return, or least risky return. Not sure if some might think that anti-Mustachian, but not everyone is trying to get to FI ASAP at all costs, even if it means investing contrary to what they feel is an "ethical imperative" like OP. It is good to point out potential drawbacks, but those may be acceptable to some.
I believe in the diversification and low costs of index funds, but I personally don't want to be part owner in a company engaged in the extraction or refining of fossil fuels which I believe need to stay in the ground. I'm willing to accept slightly lower returns, though it is not clear to me that I'll have to. Before you call me a hypocrite, I recognize I still rely on fossil fuels daily for most aspects of my modern existence. But this is no reason to give up and not try to facilitate changes for the better! I'm also trying to make other changes in my life to reduce fossil fuel reliance and CO2 emissions. Efficient car, PV array on the roof, replaced oil furnace with electric (tied to solar). I'm trying to reach FI, and I'll drive a LOT less after FI. I don't naively think my tiny 'stache will really matter to the fossil fuel industry, but if enough individual people make this choice, that can at least generate some meaningful discussion and be a catalyst for change. I have a better chance at succeeding there than owning a company whose product I'm phasing out of my life and trying to convince them they should listen to me and not extract and sell there proven oil/coal/gas reserves (their core business). Not sure why anyone would think that could be effective. To me that is like voting for a politician I disagree with and then trying to meet with her saying she should do everything differently because I voted for her. If you really think that will work, please explain.
I've found this link useful in determining how much fossil fuel exposure a given fund has:
http://fossilfreefunds.org/funds. It doesn't have all investment options, but many big ones are there. I found some of the funds I held in my 401k held up to 15% fossil fuel companies (international stock fund), others were as low as 1.5%.
A big thanks to those who provided some options to research further.
There are some socially responsible funds out there trying to beat the market, but they of course have high costs, many even higher than other actively managed funds which can pick from any company, not restricted by industry. One example is PARWX, 0.95% expense ratio. I personally have chosen to split among Vanguard Sector ETFs that do not include energy or utilities. I'm not sure the best way to balance among these since not all sectors are the same size, but I've taken a shot to divide it without what I consider being overweighted in one sector. I'm open to any suggests on that.
VNQ for REIT
VHT for Health Care
VGT for IT
VDC for Consumer Staples
VCR for Consumer Discretionary
VOX for Telecom
VHF for Financial Services