I think in Spain they say "tener(le) asco a algo", while in Mexico it's more common to say "dar algo asco".
For "tener asco", the right construction should be "no le tengo asco", because this is an indirect object.
Also, depending on the context, there may be some other expressions:
- No me disgusta.
- No me molesta.
- No tengo escrúpulo. (Although this is for a higher register maybe.)
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