Safari never seems to match POST items in the push cache, so allowing them to be pushed is a waste of bandwidth.
Firefox and Edge currently reject pushed POST requests.
I built a little test suite thing for this: https://github.com/jakearchibald/http2-push-test/
The test is served at /push-post/. /push-post/ is pushed with method POST, but making a post request to this URL does not match it.
Oh, it's also a violation of the spec, since POST requests aren't "safe" http://httpwg.org/specs/rfc7540.html#PushResources