I can't really speak for the Parthian/Arsacid empire as much as I'd like, though it's my understanding that their proximity (chronologically and geographically) to the Seleucid empire naturally led to Hellenistic influences working their way into society.

Rather than pushing out the other (with some situational exceptions), Sassanian Iran drew from its surroundings willingly and freely. There were, of course, the core Iranian values and beliefs, but Zoroastrianism did not exist at the expense of other cultures or religions (except politically at times). Even then, it was more of an issue of Christians in Sassanian Iran after some emperor from the Eastern Roman Empire whose name I cannot recall declared himself leader of all Christians. Although it did have its moments of persecuting other religions. Still much better than being in the Eastern Roman Empire.

But more to your point: Hellenistic depictions and ideas are present in Parthian and Sassanian art—heck, the diadem in the many investiture reliefs is a sure enough indication. When it comes to Greek polytheism in particular, I'm afraid I can't say. I can say, however, that the Sassanian empire welcomed religions into its fold, as evidenced by the Talmud, Nestorian Church, and several Kings of Kings. So if Greek polytheism was still around at the time, I'd wager it got along nicely. The only exceptions I can think of are Sassanian dichotomies and the issues with Christianity that I mentioned earlier.