There isn't much evidence of this. The Securities and Exchange Commission in the United States has been levying significant fines to a number of ESG funds that it discovered had marketed themselves as ESG funds but didn't actually make share buying and selling decisions on the basis of the ESG performance of the companies.
I think there are at least half a dozen academic studies that tend to suggest that there's no difference between the ESG quality of the companies in ESG funds and the quality of companies in non-ESG-branded funds. There have been at least three studies published in peer-reviewed papers that find the performers in ESG funds are actually worse.