The Democrat/Hillary thing is non-news in and of itself. I wouldn't bat an eye if a CEO of any other company did the exact same thing (as long as there weren't signs they were somehow exploiting the company's own reach to affect politics; there's no evidence of that for Schmidt).
The actual cause for concern here is Schmidt's strange willingness to effectively act as some kind of sleeper agent for the State Department (per Assange's writings and the interview transcript). Or perhaps an intelligence agency; it seems fairly plausible he was asked to speak to Assange as a way of gathering intelligence.
That's deeply concerning, and suggests Schmidt has a rather special relationship with the government. If he were no longer affiliated with Google/Alphabet, it'd still be shady yet not really violating any standards. But as CEO/chairman, it's a massive conflict of interest and suggests that the government likely was or is trying to exploit Google's leadership in some way.
Not that I blame the government here. If I were the CIA or NSA or State Department, I'd be trying to get my tentacles around massively influential companies, too. I only blame Schmidt for going along with it to such a degree.
After this knowledge is taken into account, Schmidt's involvement with the election seems a little weirder.
There are 3 factors here:
* An influential non-government civilian willing to do the State Department's dirty work, possibly at the behest of an intelligence agency
* An influential non-government civilian willing to devote a lot of time, resources, and technology to getting the State Department head elected President
* The chief executive of one of the world's largest companies
Any combination of 2 of these things isn't that odd. But the fact that someone was 1) acting covertly for a government agency, 2) working hard to get an important person in that agency elected, also attempting to be covert in the process, 3) is the executive chairman of Alphabet...
Even if the government isn't really doing anything malicious here, and Schmidt's involvement in these matters are all coincidental and his own ideas and purely due to his personal patriotism or love of the State Department and Hillary or whatever, it doesn't make it any less irresponsible to do all that while still acting as a powerful corporate executive. And even if that weren't so bad, it seems like something he is trying to really sweep under the rug as much as he can, which itself is very suspicious.
In short, regardless of the motives or conspiracies or lack thereof, all of these revelations make Schmidt seem very untrustworthy. It doesn't necessarily make Google as a whole less trustworthy, but it absolutely could if more leaks come out, and it also casts suspicion on other Google execs.