I don't think that's true. The cookie provision is misunderstood when you think you have to ask for consent for functional cookies. Follows from the GDPR, and there is no specific cookie law actually implemented in european countries. See also https://gdpr.eu/cookies/. Ah, but maybe I misunderstood and you are only talking about the cookie set by the embed?
These are the guidelines on consent exemption by the Article 29 Working Party (the European Data Protection Board's predecessor) that explain it: https://ec.europa.eu/justice/article-29/documentation/opinio...
However:
> This is not the case for cookies placed by Instagram embeds.
Yeah, I can see how this is complicated and how it fits the topic. It's not a third party cookie for the embed, but for the website it might be, and is it even a functional cookie? I doubt it. I'm not sure how those would be judged and what is a reasonable way to work with embeds. It's only certain that there is not a solution as easy as it was in this case, where self-hosting the fonts was possible.
Other than court judgments, the Article 29 Working Party opinion is the most authoritative opinion you will get on the interpretation of the e-Privacy Directive, which is the "real legislation" that you need to look at.
edit: Nobody claims that the e-Privacy Regulation is in effect, by the way -- of course it isn't, it hasn't even been passed. The cookie consent clause of the e-Privacy Directive is however in effect, and has been since 2009.
Edit: No, I'm not. The GDPR page I linked states the situation that follows both from the GDPR and the e-Privacy Directive. It also fits to what is written in the directive itself.
Everything sqrt2 says in the comments is entirely correct, as far as I can tell.
Ridiculous to govern non-privacy relevant tech usage like this. I still think that's illegal where I live. Regardless, let's hope the e-Privacy Regulation or future court decisions solve this.
If you want to make sure that you're not getting the balancing test wrong, you can always go for the legal basis of last resort: consent. Just ask the user whether you can load content from Instagram and only do it if they agree. In fact, since in parallel to the question of your legal basis under GDPR, you also have to comply with the cookie provision from the e-Privacy Directive, where there is no "legitimate interest" exception to the requirement to ask for consent, you will have to ask for consent anyway (as Instagram embeds place cookies).