These letters are issued if there has been any sort of questionable activity or sort of fraud involving your social security number or identity.  It is intended to protect you from further issues.

Taxpayer guide to Identity Theft from the IRS

If you have not filed your 2020 tax return as you are waiting on the letter, the IRS will use the latest tax return on file to make your third stimulus payment.  

How will the 3rd stimulus affect me

This doesn’t quite answer my question, I’m wanting to know if me still having to verify my identity cause issues with me getting the third stimulus payment? Will it be delayed like my tax refund is? Or will the send it anyways?

@JotikaT2 

It is possible, if not likely, that your verification issue could cause a delay in receiving your stimulus check.