In a world where capital markets are infinitely deep there shouldn't be any price response to capital and so we wouldn't expect any consequences on firm behavior. There is some good empirical evidence for slow moving capital so that's probably not true. Ethical investing is likely to drive up capital costs at least some. In which case your question boils down to two questions, "can an non-ethical company become an ethical one" and one that may seem quite different, "what is the elasticity of demand for capital with respect to the price of capital?" Tobacco and munitions companies can shift into other business but they can't get ethical investment funds without abandoning that business. Other businesses like fair-trade coffee and certified conflict-free diamonds, may allow ethical investing in the current business with higher costs. The former group really only have one choice, to shrink in response to expensive capital. The latter group have a second option, to shift into ethical investing business models that may be more expensive but less expensive than the increase in the cost of capital.
Let's ignore that first channel for a minute. Let's just consider a world with some ethical industries and some non-ethical ones. One day some people wake up and become ethical investors and this causes a change in the demand for non-ethical securities. If firms have an inelastic demand for capital (lower right graph, moving from $S_2$ to $S_1$) then the quantity of capital demanded changes relatively little from the ethical preference shock and so the total capital invested in the non-ethical industry changes very little ($Q_2$ to $Q_1$). Instead returns go up a lot ($P_2$ to $P_1$) for those investors who remain invested in non-ethical industries.
On the other hand, if capital demand is quite inelastic (lower left graph, moving from $S_2$ curve to $S_1$)), the return on capital changes very little ($P_2$ to $P_1$) but the total capital invested in non-ethical industries falls a lot ($Q_2$ to $Q_1$). In that world the ethical industries crowd out the non-ethical ones because the profits aren't there to preserve their capital supply.
Now consider production shifting. If substitution into ethical practice is more expensive than paying a higher cost of capital, this won't be an important channel. Firms are better of taking their licks in the capital markets. However, if substitution is cheaper (like when capital demand is inelastic and and substitution easy) then behavioral adaption will become the dominant channel.
In practice, according to Does Ethical Investing Impose a Cost Upon the Firm? A Theoretical Perspective by James J. Angel and Pietra Rivoli (1997), the actual effects on capital costs and quantities are quite small, suggesting that neither industry shrinking nor industry transformation are important under prevailing circumstances. If more money shifts into ethical investing this could easily change.