Officers from Hampshire and Isle of Wight Constabulary were sent to the town on Tuesday to police a peaceful protest.
Police arrested six people, and on Wednesday said three individuals had been charged.
Shannon Dodds, 32, of Gosport, has been charged with two counts of assault by beating of an emergency worker.
Sally Pearson, 31, also from Gosport, has been charged with assault by beating of an emergency worker and a racially aggravated public order offence.
Both have been remanded into custody to appear at Portsmouth Magistrates’ Court on Thursday.
Toby Matthews, 33, of Forton Road, Gosport, has been charged with common assault of an emergency worker. He has been bailed to appear at Portsmouth Magistrates’ Court on 9 November.
Meanwhile, a 19-year-old man and a 36-year-old man from Salisbury, Wiltshire, who were arrested on suspicion of aggravated trespass, have been bailed until 22 December.
A 67-year-old man from Gosport was handed a fixed penalty notice for driving without due care and attention.
Police said he was also arrested on suspicion of assaulting an emergency worker. He has also been bailed until December 22.
Some of the demonstrators in Gosport wore black clothing and face coverings, and chanted “send them back”, wrongly assuming the boat would be guided to the Hampshire coast.
The vessel had in fact docked in Dover, Kent, at about 12.30am on Wednesday, after 51 migrants on board reportedly refused assistance from a French ship and spent 33 hours at sea.
In a video published on X on Wednesday morning, far-right campaigner Daniel Thomas said of the latest migrant arrivals that it was a “sad day for the country”, but argued that pressure from demonstrators “worked in some respects” because it stopped arrivals coming into Gosport.
Meanwhile, Home Secretary Shabana Mahmood on Wednesday ordered an “urgent review” after the Border Force failed to intercept a second migrant boat in two days before it reached the Kent coast.
Border Security Command has detained 21 people following a boat arrival on the beach of Samphire Hoe, Dover, on Tuesday afternoon, and the Home Office has not said whether more people are being sought.
It comes after a dinghy made it to shore at Folkestone on Monday morning, which was the first undetected arrival for over a year.
In a statement on Wednesday, Ms Mahmood described the undetected crossings of two small boats this week as “not acceptable” and said the Border Security Command is investigating.
“Our improved monitoring has led to uncontrolled crossings becoming incredibly rare. But even one is one too many,” the home secretary said.
“That is why I have ordered an urgent review by the Border Security Command into how this happened, and what must be done to ensure it doesn’t happen again.”
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