I was experiencing the exact same problem this morning trying to log into banking. Of course, I did not override the Kaspersky warning. This happened in the Chrome browser, which I always use. I tried logging in with Internet Explorer (again, using the Safe Money), but to no avail as I got the same pop up saying it wasn't advisable to proceed (certificate verification problem). I cleared the cache of both browsers, but that didn't make any difference. The error code along with the certificate verification notice was 0x000000f., just like everyone else's.
For whatever reason, I rebooted my computer, & tried to sign into the banking site again using the safe money. Lo & behold, the protected browser (green frame) came up, & of course there wasn't any certificate warning. It was as though there was never a problem.
I had reinstalled the KIS back in March/2019 at the prompting of Kaspersky Tech Support. They advised there was a problem, & redownloading would resolve the issue. They provided a link for me to use.
Here I was yet again, having a problem.
C'mon Kaspersky, you're the best out there. Let's get these issues resolved!!!