Can I short say exxon mobile to get rid of any profits i would make from the mutual fund?
I have a hard time finding diversity without investing in companies that go against my principles.
That approach would turn your low cost index fund into a ridiculously expensive non-index fund. Are you really going to track the number of shares for each stock you don't like (for whatever reason), including new additions and dividend reinvestment?
There are socially responsible funds/ETFs, and a newer class of funds/ETFs labeled "sustainable". Do some research on Morningstar to see if you can find one that suits your preferences.
You might also be amused that there is a Vice fund (VICEX) that invests in alcohol, tobacco, firearms, etc. It is outperforming the S&P 500 year to date, and roughly matches it over 5 years.
So dump your mutual fund(s), and buy your own stocks.