You say that, but 0.0000000000000001% of even the world's largest company by market cap (Apple, at 592.44B) would be $0.000000560337
if you ever so much as glance at an ad an evil company runs, then assuming a CPM of $0.01 (two orders of magnitude lower than actual average cost), your single glance is worth $0.00001 or 17 times the value you said you would never hold.
So you'd never hold $0.0000000000000001% of an evil company but you are more than happy to just give them 17 times that value for free by glancing at one of their ads at some point in your life?
You need to lower your purity standards if you don't want to be a hypocrite :)
EDIT: all right, I mixed my metaphor. just think of an evil ad company :)
But yeah, the 0.xxx1% percentage was just exaggeration :P
I applaud you for your principled stance but you should be aware of all the consequences.
(Another term for this is "socially responsible investing" and there are indexes, and associated high-fee funds, that claim to seek it. However, I feel this is a very personal issue; I wouldn't use such an index because someone's definition of socially responsible/non-evil may be very different from mine. My opinion is such indexes/funds are just gimmicks with high expense ratios.)
And even if such an approach will most likely lead to lower returns (for example, due to higher fees in paying commissions, though that can be reduced or eliminated by smartly taking advantage of brokerage promos), I'm fine with that. I'll take my $1.00 earned from what I consider to be ethical means vs. $10.00 earned from what I consider to be unethical means.