- both have backgrounds as tradesfolk - Trump is a 'businessman' and Thatcher was the daughter of a grocer
- both (partly as a result) are not merely anti-Establishment, they are outsiders in their own parties (Thatcher was loathed by the patrician class of old-school Tories)
- both arrive as vigorous reformers against a background of (real or perceived) ossification (in Thatcher's case the background was post-World War II corporatism, the 'sick man of Europe' label, the winter of discontent etc; in Trump's case, the failure of the US Establishment to distribute the benefits of globalisation, the failure to control its debt etc)
- both evoke extreme reactions among both the general public and the commentariat - there is no middle ground with either of them, people either love them or hate them
- both have a weird thing with hair
Make of it what you will.