Impossible to set priority for alsasink thread.
There are instructions how to set thread priority: https://gstreamer.freedesktop.org/documentation/application-development/advanced/threads.html
In order for this to work gst_message_get_stream_status_object (message) has to return GSTask object so it can be given custom GstTaskPool.
It's impossible to do that for alsasink because alsasink never reports GST_STREAM_STATUS_TYPE_CREATE, only GST_STREAM_STATUS_TYPE_ENTER and even when it does that gst_message_get_stream_status_object (message) is of type GThread, not GstTask.
Can this be changed in any way (some configuration or even patching some class and recompile)?
Setting real-time priority makes the most sense for elements like alsasink which are closest to output devices and alsasink is only element you cannot do this with now.