They're right, but they're presenting it in a way as if the toxicity of AGPL is the actual truth, and not just the opinion of greedy corporations.

Being toxic to greedy corporations but beneficial to everyone else is the point of the GPL licenses.

But it’s not only toxic to the greedy corporations but all the others as well, hence

Why is it toxic for me to need to push my code to a git repo if I start using it in my services, if I'm not trying to act as a for-profit corporation?

You can totally make profits by selling services based on AGPL code btw, it's completely fine. As long as you redistribute your derivative work as AGPL too.

There's nothing toxic in the AGPL for you as long as you don't want to make that code proprietary (even without making profits)

No. There's no restriction of usage in the (A)GPL. Anyone, including big corps, can use AGPL software. Preventing them to use the software is not the point neither. The point is trying to ensure end user freedom.

They just choose avoid agpl software. Their loss. Unfortunately they also spread FUD on this and many commenters here happily convey it.

How so? You might be thinking of SSPL.