Tory members back the death penalty, believe Islam is a threat to the British way of life and think Donald Trump would make a good prime minister, according to a poll.
The YouGov survey suggested 58% believed the death penalty should be allowed for certain crimes, against 37% who did not back capital punishment.
Some 56% of those surveyed thought Islam was "generally a threat" to the British way of life and just 22% thought it was "generally compatible".
On the question of Mr Trump's leadership, 54% said they believed he would make a good prime minister, with 43% saying he would be bad.
YouGov questioned 892 of the Tory members who will be choosing between Boris Johnson and Jeremy Hunt to decide the next prime minister.
The survey, for Channel 4's Dispatches, found 42% thought having people from a wide variety of racial and cultural backgrounds has damaged British society, 49% said schools should not be required to educate children about LGBT relationships and 51% thought most people on benefits could get a job if they tried hard enough.
Some 46% said concerns about climate change had been exaggerated, while 45% said the threat is every bit as real as scientists have said.
The pollster questioned members between June 11 and 14.
A later study, carried out after Mr Johnson and Mr Hunt had made it through to the final stage of the process, found the majority of members thought the former London mayor would make the "most trustworthy" prime minister.
The poll of 1,119 members carried out between July 1 and 5 found 52% backed Mr Johnson to make the most trustworthy premier, with 32% favouring Mr Hunt.
The programme, which will be broadcast at 8pm on Monday, also highlights Islamophobic posts on Facebook from self-identifying members of the Conservative Party.
One member of the Boris Johnson Supporters Group said: "I would ban all Muslim (sic) from entering the whole of Great Britain."
A member of the Jacob Rees Mogg Appreciation Society said: "Two mega mosques agreed planning permission in Maidstone and Worcester, how we feel about this?" Another person posted: "WRONG."
They are among a series of social media posts highlighted by the programme.
A Conservative spokesman told the programme: "Those people making these posts that we have found to be members of the party have been suspended pending investigation.
"Discrimination or abuse of any kind is wrong and will not be tolerated."
Mr Rees-Mogg told Dispatches the Facebook group is not an official supporters' group, saying: "I absolutely condemn such behaviour.
"Anyone who behaves in such a way is not one of my supporters and should be reported."