All those constructions, and some more besides, are completely acceptable and standard.
The verb form
(predisposed to or predispose [someone or something] to)
The OED has all three possibilities among the examples it lists:
Tristy was p̲r̲e̲d̲i̲s̲p̲o̲s̲e̲d̲ ̲t̲o̲ ̲b̲e̲l̲i̲e̲v̲e̲ that Van Gogh must have been a determined and inveterate ‘faker’.
We have not even a word in English for the complex of psychological elements which p̲r̲e̲d̲i̲s̲p̲o̲s̲e̲s̲ ̲u̲s̲ ̲t̲o̲ ̲f̲o̲r̲g̲e̲t̲t̲i̲n̲g̲.
Noun phrase (NP):
New Yorkers..are always p̲r̲e̲d̲i̲s̲p̲o̲s̲e̲d̲ ̲t̲o̲ ̲d̲r̲a̲m̲a̲-̲q̲u̲e̲e̲n̲ ̲s̲e̲l̲f̲-̲i̲m̲p̲o̲r̲t̲a̲n̲c̲e̲.
The noun form
The OED has the following:
One of the few indicators of a possible p̲r̲e̲d̲i̲s̲p̲o̲s̲i̲t̲i̲o̲n̲ ̲t̲o̲ ̲m̲e̲n̲t̲a̲l̲ ̲i̲l̲l̲n̲e̲s̲s̲ in a given individual is a positive family history of such illness.
There was a strong p̲r̲e̲d̲i̲s̲p̲o̲s̲i̲t̲i̲o̲n̲ ̲t̲o̲ ̲b̲e̲l̲i̲e̲v̲e̲ that China's culture..was dynamic and changing in nature.
But in published literature (i.e. if one searches google books for the underlined phrase, below), one can easily find
A psychological p̲r̲e̲d̲i̲s̲p̲o̲s̲i̲t̲i̲o̲n̲ ̲t̲o̲ ̲b̲e̲l̲i̲e̲v̲i̲n̲g̲ in moralizing gods could then be favored by natural selection within groups.
The p̲r̲e̲d̲i̲s̲p̲o̲s̲i̲t̲i̲o̲n̲ ̲t̲o̲ ̲f̲a̲l̲l̲i̲n̲g̲ ̲b̲a̲c̲k̲w̲a̲r̲d̲ may result from a smaller posterior than anterior base of support.
If you adopt a dog with this type of genetic p̲r̲e̲d̲i̲s̲p̲o̲s̲i̲t̲i̲o̲n̲ ̲t̲o̲ ̲f̲i̲g̲h̲t̲i̲n̲g̲, you must...