iOS wants to access your google account

It would be better if you can please re-post with a screenshot, in order to understand the phenomenon better. Images/pictures speak louder than words. 

Please understand this is a public forum: While attaching a Screenshot, do not provide any personal credentials, such as IP address, Card detail, email id, apple id, IMEI number, Serial Number, Phone number, Order ID, if you are sharing a map ensure your location is not identifiable, etc.

With the limited information that you have provided, It is hard to even guess the problems faced by you. 

You may get faster and better responses to your query by --> Writing an effective Apple Support Commun… - Apple ...

Please re-post with detail so that someone else can help.

It’s perfectly normal for Mail to access all those things if you’re using Mail to access your Google data. Google is asking the questions.

Google is not an Apple product. Contact the app developer here --> App Support or Google Support