The website tried to rely on legitimate interest as the legal basis for processing the data, and that precisely requires a balancing test between the interests of the website host and the interests of the data subject.
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).
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).