The phrase "a real distrust" is correct and usable in written English.
It can be used to emphasize the genuineness or intensity of distrust someone feels towards a person, situation, or concept.
Example: "There was a real distrust among the team members after the incident, making collaboration difficult."
Alternatives: "a genuine distrust" or "a significant distrust".
The problem is, the reason you can't help but feel pressure to give him the benefit of the doubt or vote for him reluctantly is that you feel a profound and real distrust towards Hillary Clinton.
There is also real distrust in the churches about whether the money that would come would be sufficient to provide for the needed staff and services.
"I think the recording device suggests a real level of distrust".
"There's a real and understandable distrust of technology as a shortcut for good clinical skills," said Albert Rizzo, a psychologist at the University of Southern California, "but I think, deep down, most therapists will want any tool that can help them do their work, and they'll be open to using virtual approaches".
But if publicizing a doctrine generates distrust from a real audience merely because of people's attraction for simplicity or non-demandingness, the frustration flowing from such a distrust should hardly be considered relevant to the assessment of the maxim's (in)justice.
The Bush administration's vision blends a real, if limited, internationalism with the reflexive conservative distrust of government, particularly one in which presumptuous foreigners try to constrain the United States.
In The Driller Killer, Ferrara's distrust of fakery went as far using a real drill-bit.
Adding to the general distrust that Mr. Saleh's decree represented a real concession, the decree made no mention of delegating control of the armed forces, which Mr. Saleh's family dominates through its leadership of several elite divisions.
The trust value that node X evaluates towards node Y at time t, Txy(t), is represented as a real number in the range of [0, 1] where 0 indicates distrust and 1 complete trust.
