So, is it some kind of poetic freedom to omit the subject like this? 

Lyric writers usually feel free to do whatever they can to achieve a mood, a feeling, a meaning within the context of the music. Like poetic freedom on steroids - poetic freedom taken even further - all "in my opinion", of course :)

Like "we are free to".

But I really don't think that is what is happening here, grammatically.The subject is the "we" at the end of the line, and the opening phrase up to the comma is really a parenthetical phrase - hence the comma. But the meaning would be the same if we rewrote it as We are free to associate, and the bonds that we create ..."

Or is it an inversion+verb omission, "the bonds that we create are free to associate"?

I'm pretty confident that is "we" who are free, not the bonds ... but I could be wrong :)

(Like from another song "frivolous gavel our design, ludicrous our threat") - From Rancid, the Positive Aspects of Negative Thinking.

I don't know this other song either, but I'm afraid "frivolous gavel" looks like a nonsense phrase to me, picked for its metre and sound. A gavel is a small wooden hammer, as used by a judge or auctioneer, and there's no universe I know where small wooden objects can take on personailty traits like frivolity! "That's a playful doorknob" ..hmm.  Let's say that's a charmingly playful lyric! 

That's a nice interpretation, I've never thought about it that way. To me, it's about mostly social relationships, how these disguises and fake personalities can be more effective or how can be more misunderstanding due to the Internet. And the irony that while the social web connects us all, we feel more isolated and left out than before. Mainly because of other parts of the lyrics.
And the chorus fits here as either describing the situation or suggesting a solution.

But I'm glad to know that smth at stake can mean that the worse outcome is having that smth(opposed to "with our lives at stake", which wouldn't mean "oh no, we might stay alive" :D)

So, is it some kind of poetic freedom to omit the subject like this?
Like "we are free to".
Or is it an inversion+verb omission, "the bonds that we create are free to associate"?
(Like from another song "frivolous gavel our design, ludicrous our threat")

That song sounds really cleansing indeed:) It's like too calm:D

I hadn't heard this song before.

To my mind, this seems like a song about the bitterness of using deception to achieve physical intimacy ... a sense of self-disgust at the depths we may stoop to to seduce someone. The "sweet poison" spools out of your mouth,  as you seek something based not on who you are but on what you think your "victim" wants to hear ...

on

"Free to associate, the bonds that we create

might make more sense with the extra comma. We are free to associate - to seek new friendships, new relationships.  "The bonds that we create" - the new relationships we form - "With pretense at stake" - while we are pouring out our sweet lies, our beautiful words that are rarely truthful,  "At stake" - this forms part of a three -step near-rhyme, or assonance, with "associate" and "create", which, structurally, releases into  "exceed our limits". I wonder if it's been chosen mainly for this sound property. In terms of meaning : "with pretense at stake" - we are investing lies to create a new (and, we hope, seductive) persona - and the truth would destroy both persona and the chance of winning someone over.

"Exceed our limits" refers back, I think, to "Free to associate", which I read as self-description. It is "the bonds that we create" that will "exceed our limits" - we are trying to seduce, form bonds with more people than we have capacity for, or than we have a legal limit for ...

But this is poetry, really, sort of anyway. What does it mean to you? That's probably what matters.

Just my opinion. I'm not really into metal :)  Here's  a sweet little song, that may cleanse your palate ! https://youtu.be/zb0x4_2xocY