"unquestioningly accept" is a correct and usable phrase in written English.
It means to accept something without hesitation or doubt, without questioning its validity or truth. Example: The monarch's subjects were expected to unquestioningly accept his decisions without challenging his authority.
Too many whites unquestioningly accept a system that disproportionately punishes blacks and that gives public schools serving disadvantaged children many fewer resources than those serving affluent children.
T's Culture issue, on newsstands April 14, pays tribute to the artist's inability to unquestioningly accept the society in which she lives.
Even Marine Le Pen, standard-bearer of the French far right, has ditched the notion that children should unquestioningly accept the authority of their parents.
But Ms. Woolcock and the opera's creators unquestioningly accept the injustice theory of terrorism: the idea that it is a response to a grievous wrong.
This she plays as well as she can, although the part is bafflingly underwritten and two-dimensional: we are never told how she found the Beach, and how it is that the others unquestioningly accept her (slightly shrill) authority.
It seemed a more honest, rebellious way of understanding the world: you didn't have to unquestioningly accept what your school and parents were teaching – or omitting to teach – you.
Joseph unquestioningly accepted Carvalho's version of these events.
Expertise, of whatever sort, is no longer unquestioningly accepted.
It is unquestioningly accepted at home and widely used beyond the euro area's borders.
For years, his investors gratefully and unquestioningly accepted returns that were strictly incredible.
Its judgment, incidentally, was once unquestioningly accepted by a rival who was bringing suit.
