Bank accounts for dual citizen babies- tax/legal issues?

I wasn't sure to post this here, or Parenting section but...

Any advice on US and UK savings accounts for dual citizen babies?

I am wary of starting savings accounts in the US and UK for our babies, as I don't want to saddle them (or me) with future tax burdens.

My parents in the US are asking us for the babies' SSNs (which we just got), so they can start some kind of savings account for them. (I had no idea that grandparents had the legal right to do that, but apparently they do).

And relatives in the UK have given us money, and encouraged us to start UK savings accounts for them.

UK: What accounts have you parents started for kids?
All I know is that ISA accounts in the UK, even cash ISAs, are taxed in the US. So guessing I should not open an ISA account for them? As this will create a future tax burden when they have to start filing taxes for the US.

US: What accounts have you or grandparents started for kids?
Are there any tax or legal issues I should know about?

Also is it a problem that if my parents start a US account for the babies, their names will be associated with an address in the US? Especially an address in a state different from my (absentee ballot voting address)?
Thanks!

If you plan to have your children attend a US university, consider having you or your parents open a 529 Savings Plan. Investment grows tax free for educational expenses which now with Trump’s new tax law include expenses K-12th grade up to $10,000 pet year. However, you need to confirm if your home state will follow the new tax law.

Another option you may want to consider if you want to avoid filing tax returns is have your parents open a savings or invest account under their name with your child as beneficiary. However, any tax liability falls on them. Consider tax-exempt municipal bonds. You would avoid federal taxes. State taxes would be dependent on state you lived and bonds held.

My kid's just have straight forward children's savings accounts.  No frills or interest to get excited about.  My name is on their accounts so I do have to do FBAR's each year.

Ha ha!  Grandparents contributing to savings accounts?  Good one!     I jest, we don't have "that kind" of grandparents.  If we did, I would explore the 529 accounts in the USA and I'd love to see if my kids would qualified for Florida Prepaid.  I should just look into that one night.   

US Savings Bonds?

If you plan to have your children attend a US university, consider having you or your parents open a 529 Savings Plan. Investment grows tax free for educational expenses which now with Trump’s new tax law include expenses K-12th grade up to $10,000 pet year. However, you need to confirm if your home state will follow the new tax law.

Another option you may want to consider if you want to avoid filing tax returns is have your parents open a savings or invest account under their name with your child as beneficiary. However, any tax liability falls on them. Consider tax-exempt municipal bonds. You would avoid federal taxes. State taxes would be dependent on state you lived and bonds held.

US tax exempt municipal bonds remain UK taxable, so are an unusual choice for a UK resident. A 529 plan would have no effect for UK purposes so income and gains within it might be reportable & UK taxable.

US tax-exempt municipal bonds is a suggestion for investment accounts grandparents living in the US could have with grandchildren as BENEFICIARIES.  Income from account would not create a tax liability for parent living in the UK.

529 plan - Grandparents can also own these accounts which benefit the grandchildren and would not impact tax liability of parent living in the UK.