An ISA is one of the cleanest tax shelters available to a UK resident. To the IRS it is not a shelter at all. There is no US recognition of the wrapper, so income and gains inside it are simply taxable to you as a US person in the year they arise.
That alone would be an annoyance. The real problem is what the ISA holds — and the regime the US applies to it.
Why the funds inside are the real issue

Unit trusts, OEICs, investment trusts and most non-US ETFs are almost all Passive Foreign Investment Companies under US rules — the test is mechanical and pooled funds pass it by construction. Default PFIC treatment spreads a gain across your holding period, taxes each slice at that year's top ordinary rate, and adds an interest charge on the 'late' tax.
Held long enough, the effective rate on a PFIC gain routinely exceeds 50% — on an investment that would have been lightly taxed on either side of the Atlantic alone. The reporting burden, Form 8621 per fund per year, is disproportionate to the sums involved even when no tax is due.
The elections, and their timing
There are elections that improve matters. Mark-to-market is the most commonly useful for listed holdings — gains are taxed annually as ordinary income, which is worse than capital gains treatment but far better than the default regime. A QEF election is cleaner still but requires fund-published data that UK retail funds rarely provide.
Both generally have to be made in the right year — usually the first year of holding or the first year of US personhood. That is why this is worth looking at before a position has been held and grown for a decade, when every year of delay adds to the eventual interest charge.
What a clean portfolio looks like

None of this means a US person in the UK cannot invest. Shares in an ordinary operating company are not PFICs — though a foreign company that is itself mostly cash or investments can be one, so holding companies deserve a second look. US-domiciled ETFs that hold HMRC 'reporting fund' status are treated rationally by both systems, and they exist for every major index. Cash ISAs still do their UK job — HMRC leaves the interest alone — but the US taxes it with no UK tax paid to credit against, so the wrapper saves nothing on that side.
For an existing PFIC portfolio, the honest arithmetic is often a planned purge: realise the positions, pay the historic charge once, and rebuild in clean funds. The wrong move is doing nothing while the interest clock runs. We model the cost of leaving against staying before recommending either.
