Given the number of antivirus products available, it's a whole lot easier to dismiss Kaspersky as a precaution than try to sift through the "facts" to determine if it's actually dodgy. Then you only have to be concerned about ties to US intelligence.
Whether they are demonizing Russia or not (they are), it's up to their own discretion to use a different AV software. It's not like anything bad could come out of The US government's concern for their own security. It is ironic though.
Then again, it's not like you can trust any AV. I recall an eastern Slovakian company creating an AV they would boast how it was the only one that could identify and remove the infamous OneHalf (a.k.a "Slovak Bomber") virus, only for it to later turn out that they were the ones who created said virus.
And of course these guys also got to work at ESET later on (afaik). Take this as a lesson...
I guess you can go with Trend Micro. They are a Japanese company. Japan seems to be content minding its own business. Really how can you know any AV is truly safe from backdoors.
I wonder why the FBI is investigating? This seems more like the territory of the CIA or NSA. Doesn't the FBI have enough on its plate investigating federal crimes committed by people within this country?