ME2 Liara demonstrates a complete lack of morality and sufficient ruthless ambition during LotSB too. So much that Shepard even questions her behaviour. Liara will respond to that, but it only shows that she's good at alleviating Shepard's concerns verbally - just like TIM is.
The only difference between ME2 Liara and TIM is that she'd romance Shepard and use it to her advantage. That, and the writer bias.
Afterwards, she's dreaming of starting a war with that power, and she declares so outright in Shepard's presence. A war with a third party is something that the galaxy most certainly doesn't need during the Reaper invasion. What if the Reapers are attracted by the SB's power, warlike activity, and closeness to Shepard? Why would you give the most power in the galaxy to such an obviously dangerous person?
It's just your luck that LotSB doesn't have a choice at the end, with the option of giving Liara the SB marked as red, and that the writers don't have all your companions (even those who have never met Liara and know nothing about her and her with Shepard relationship) say that they have a very, very bad feeling about giving Liara the SB base.
There are no in-game choices to make regarding Liara and the Shadow Broker, as you said, hence your comparison is irrelevant. Although you're reaching so hard regardless I can hear your tendons snapping. Especially with "writer bias;" not only did different people write the characters, so far as I know, but they're also the ones who created the characters to begin with. If Liara is written to be less evil than TIM, than that's the truth of it.
But if I must address your other points... the major difference is that I knew Liara during ME1, where she demonstrated ample morality and suchlike. If it was suppressed in ME2, that's regrettable, but I know that there's something there to unsuppress if I have to. I have no such guarantee, or in fact any bare hints, with TIM. And Liara's ruthlessness seems to have faded sufficiently by the end in any case. Finally, Liara lets me into the nerve center of her operations regularly and allows me to see what she's up to; I can even undertake some operations myself. No such reciprocity exists with TIM.
Well the former not so much. Shepard is given hints to assume that he is machiavellian in his ways but that doesn't equal immorality. As for the latter, yes however with a but. Yes he has shown to be ambitious but his ambitions have shown to be always be in the better interests of humanity. Never is there a moment that hints that his goals are purely self serving.
He's never shown that he possesses morals at all. He's never taken a single altrustic action that wasn't for Shepard's benefit somehow, and Shepard is his own pawn, so that doesn't count. I've never had the slightest hint that he's in any way trustworthy; he's an accomplished liar and manipulator, in fact outright declaring it with his title. He tells me the bare minimum of what I need to know and gives me no kind of hint as to what Cerberus is doing elsewhere, or how exactly this technology is going to be applied. There's nothing whatsoever to trust.
As for other stuff that's more tied to Cerberus such as Teltin and so on: Every piece of information Shepard receives on these things shows that TIM was ignorant of the happenings, not involved with the happenings, was against what happened and then made the proper measures to make sure they didn't happen again.
Again, nothing to trust. Illusive, remember. I don't doubt that TIM disliked Teltin's enormously high burn rate, which is why the scientists were hiding it, but actually caring for the suffering of the prisoners? Not in ten thousand years.
So again, what exactly led your Shepard to distrust TIM so much that she'd potentially doom the galaxy? What can she point to and say "that's why". Also, how has he earned such levels of distrust and yet the Council has your loyalty.
Because I believe the galaxy is more likely to be doomed by giving Cerberus the base. It's not a moral issue. And it's not quite a matter of just earning distrust, it's that and never earning trust.
The Council has proven themselves to be ruthless, ambitious and self-serving above anything else. What makes them different?
The Council is a means to an end. I work for them, for the most part, because they haven't done much to hinder me in my mission to do the most good for the galaxy. And when they did, at the end of ME1, I disobeyed them.