If the LLC is setup as passthrough as a single foreign member and the actual (100%) work/service is not done within USA borders then US IRS will not care to︀ tax the LLC member or the LLC entity.
But of course, as you say, Spain,︁ and I believe most jurisdictions in EU whereever the LLC member is a tax payer︂ will want to get the income taxed.
I'm not sure I understand why Spain would︃ tax a US disregarded entity that has passthrough income?
Logically they would tax the Spanish︄ members income from the US LLC, since the member is also a Spanish tax payer.︅
I understand if Spain has something similar setup as the US GILTI model and the︆ LLC elects to tax as a C-corp.
But not as a disregarded entity due to︇ the US tax return of the LLC would not give the Spanish tax authorities any︈ profit or loss to calculate any tax on (since passthrough profit and loss is found︉ on LLC members tax return, not the LLC's)?
So I see the taxation only on︊ the tax members tax return where ever he/she is a tax payer and the LLC︋ stays as disregarded as well, US or outside.