I'm not astigmatic, but I do need corrective lens for my short-sight.
I wear glasses most of the time, simply out of convenience, but if I am going out particularly for birding, then I use soft contacts.
Whilst I frequently use my binoculars whilst wearing glasses, wearing contacts does have two major advantages in my opinion.
Firstly, my glasses steam up very easily, especially if I am hot, which hampers seeing in general, but is worsened by using binoculars.
I think the close contact of my bins and my hands against my face restricts whatever airflow there might be, resulting in lens-fogging.
I know that contacts can fog, but it has never happend to me.
Secondly, with the eye cups extended on the eyepieces, extraneous surrounding light is blocked out, and so the image I see through the binoculars is significantly clearer.