I think that the optimal solution to what you are describing is to push them to another platform like signal and to start lowering your activity on Instagram till you have another communication tool with them and then delete your Instagram.
If they do not want to move, then you have to choose either your privacy or their convenience .
Your use case could be covered without instagram account by the following:
Android: Feedsta
Desktop: Bibliogram
You could deactivate it at least and try to use the above for 2 weeks if it does satisfy your needs, then go on and delete it as it will benefit your privacy and mental health more than you think despite the cons of not having an account.