Are there general rules in Vedic rituals? No, just material entailments

prasaṅga is not frequent in the Śrautasūtras and I failed to find a definition of it. Hence, one has to reconstruct its meaning indirectly, through its usage in the ŚrSū, through its usage in Grammar and Mīmāṃsā and possibly also through its etymological meaning. Every translation is therefore intrinsically tentative.

In its only occurrence in the Aśvalāyana Śrautasūtra (AśvŚrSū 1.1.22) it is opposed to apavāda (certainly meaning "exception"):

prasaṅgād apavādo balīyaḥ

Mylius translates:

Eine Ausnahme (-Regel) ist gewichtiger als eine allgemeine Regel (Mylius 1994: 29a)

That is, "An exceptional [rule] is more forceful than a general rule".

But the meaning seems, more precisely, to be "default occurrence". The prasaṅga is what one expects to happen, what follows by default from the previous discussion. Only secondarily, it defines the "general" rule. Hence,

An exception is stronger than what is automatically entailed.

On prasaṅga, see here. On the problem of reconstructing the meaning of a term, when the technical context is lost, see here.