Completely depends on how she is using her Instagram. You will limit yourself (needlessly) if you take a "No Instagram" position with women because social media is such a major part of today's society.
If the woman is posting pictures of you two on it or using it for fairly innocuous reasons, there is no issue. If she is posing in sexy poses in front of her camera in her underwear or drunk photos with her girlfriends and pasting them all over the place, then yes, that is a deal-breaker for an LTR. You have to evaluate it based upon what you see.
Most women have Private Instagram accounts. The typical woman doesn't leave her Instagram on Public for anyone to see. Only big time influencers and attention whorres have Public Instagrams.
The only way that most men would see what a woman is doing on Instagram is by requesting to follow her. There's debate in a developing interaction about when in the interaction/relationship to request to follow a woman on social media.
Instagram is probably the biggest social media platform right women for women 25-40. For the 18-24s, TikTok might be where they spend more time than Instagram, though there are plenty of 25-40 year olds on TikTok. These trends can change quickly so the last sentence might not age well.
Facebook was the hot social media platform around 2006-2011, but is now mostly where older people spend time. People around my age (mid to late 30s) rarely use Facebook and that's been the case for at least 5 years. The only time I see people close to my age using Facebook is for their wedding and baby photos.
Twitter and LinkedIn are still out there too but rarely get discussed in the context of male-female dynamics. Most women who are at least semi-active on LinkedIn get offers for dates/sex on that platform. Some women will even post thirst trap pics on LinkedIn. Twitter is similar in that regard.
There is a difference between a Wanna be influencer who demands you be her photographer while she poses in a bikini and someone who occasionally posts pictures of her dog, and pretty flowers.
I've watched my Gf's social media stream change from selfies when she was single to pictures of us as a couple to infrequent pictures of sunrises as she walks the dogs in the morning. All with no input or direction from me.
I'm sure this happens regularly.
Most women are not using Instagram for butt selfies, regular selfies, and generally sexy pics. The typical woman on Instagram has a Private account and infrequently posts basic things like food/beverage pics, vacation pics, and other boring and not sexually provocative pics.