More than 50,000 people have signed up to demonstrate in London on Friday when protesters intend to fly a large balloon over parliament portraying Trump as an orange, snarling baby although a counter-gathering to welcome him is also planned.
Mr Trump has a White House doctor at his side at all times and one of five rotating military aides who carry the nuclear "football" - equipped with communication tools and a book with prepared war plans.
Trump then angered May and many Britons by retweeting unverified, anti-Islamic videos from Britain First, whose leaders have been convicted of hate crimes.
Ahead of Trump's visit, the PM said: "There is no stronger alliance than that of our special relationship with the USA and there will be no alliance more important in the years ahead".
Trump has long voiced his support for Brexit, saying it was part of a global uprising that ultimately thrust him to power, and he was at his Scottish golf resort the day after Britons voted to leave the European Union, saying the outcome was a "great thing".
According to a notice posted on the embassy's website on Tuesday, "Numerous demonstrations are being planned for July 12 to 14, 2018, surrounding" Trump's visit.
Potentially tens of thousands are expected to march to a rally in Trafalgar Square on Friday afternoon, organized by the "Stop Trump Coalition".
The US Embassy in London issued the alert ahead of Trump's arrival on Thursday after attending a North Atlantic Treaty Organisation summit.
The US president appears unpopular in Britain, where his brash style and hardline "America First" policies have caused consternation across the political spectrum and society.
On Friday, Trump will join May at a United Kingdom military demonstration at a defense site, after which they will go to May's country home Chequers for bilateral talks, according to the Evening Standard.
A statement on the USA embassy website warns USA citizens to "be aware of your surroundings (and) exercise caution if unexpectedly in the vicinity of large gatherings that may become violent".
Trump will spend the weekend at the former, which he described as a "magical place", before heading to Helsinki, Finland, for a much-anticipated summit on July 16 with Russian President Vladimir Putin.
"Donald Trump likes to pose as an global tough guy, but it looks like he's too scared to face protesters in London", the group Stand Up to Trump declared in a statement, alluding to the usa president's reported plans to steer clear of the streets of London.
So why are people so unhappy this time and why didn't Mr Trump get the state visit treatment Britain offered to Robert Mugabe?
Assistant Chief Constable Chris Shead, from the National Police Coordination Centre, said: "Police forces are working together on a significant, multi-faceted security operation supporting the presidential visit to the UK".