Is it possible to steal sensitive information from SMS?

Unless you trust the app with SMS permissions, you should not be giving the permission. Other option is to use some spoof app to spoof the SMS permission

My suggestion would be, if your sms contains really sensitive information. It will be better if you use that number on a feature phone.

You can never rely on Android for privacy. Many projects tried to overcome these limitations by sandboxing the sms/communication module and providing a fake dummy data to the system and other apps. but those are not practical solutions.

most of the people I know whose economic portfolio is quite a bit large/ transact heavy amounts through current account they use the transactional phone number in a feature phone.(ie-nokia dabba phone)

Avoid giving  sms permission  , and if necessary   ,retrive  it as soon as your work finished  with it .

If you care so much about privacy

Go with Iphone or Pixel , Samsung

Dont trust any other vendor

Bdw

Its not always related to your sms app

But other apps accessing your message read permission

Like auto detect otp

Apps like Cred etc do read your financial msg credit card statement related msg even mail to fetch your credit card bill and due date etc

If you wanna protect your msg from all those

Just use a basic mobile without internet

Thanku

Yes , if you give permission to app read your sms ... Paytm use to read my sms and give credit card alerts 

have to restrict apps 

Tbh Most sensitive data on SMS is limited, Like OTPs are only useful fpr snooper of they get it realtime..

Currently the most dangerous threat to SMS privacy is Loan Apps and Apps that monitor SMS claiming "Credit Analysis"

They are actually learning from your messages and even reading through, This was proved when shady lenders started using private data from SMS and Contacts to call people and threaten to make extra payments and such...This was the reason RBI has banned a lot of Loan Appa since they were snooping and conducting malpractices.

Best policy is don't let unwanted apps run in background, Use a strong App Hibernator, This can boost your phone performance too...

As said by others, give permission to the app only when it's fully trusted by you.

Use bouncer app - best for these issues