Remote work for non-Irish base employer while on stamp 4, reckonable residence?

Hi,
I'm on on stamp 4. I'm planning to look for remote work for non-Irish base employer (US).
1. Will it affect my renewal for the stamp 4?
2. After I have lived in Ireland for 5 years, I will apply for Irish naturalisation. Will I get rejected because I have been working for non-Irish base employer?

I'm worrying they will argue that I have job for non-Irish base employer, why do I need to renew stamp 4, or Irish naturalisation

Thanks in advance.

What's the reason for you to have a Stamp 4?

I'd be adamant to ensure you're tax compliant, since for naturalisation they would wish to know whether your taxes are in order not (seems like they ask Revenue directly now) - I'd advise you to take it up with financial adviser.
For the immigration purposes, depends on the reason of you having a Stamp 4 - if you came here via STEP program, for example, which is made to create Irish startups, to work for a US employer, chances are your visa won't be extended.

Even if you were an Irish citizen you'd need to set up either your own company or an employer of record. In the latter case you're an employee of an Irish company who consults with the US company. I did this myself for the last 5 years, it was fine.