The voicing rule for / θ / means that before a voiced consonant this phoneme merges with /d/, given that [ð] is also an allophone of /d/. Indeed, in Old Spanish the word juzgar was spelled with a d rather than a z, as were words like hallazgo ‘finding’ and portazgo ‘toll charge’ (cf. Old Spanish iudgar, falladgo and portadgo).

In English, you can say "each time that I go out" or "each time I go out", and both are acceptable and understood. In Spanish, however, you can say "cada vez que salgo", but "cada vez salgo" is incomplete and sounds odd to Spanish speakers. Why is that?

The sounds [d] and [ð] are two allophones of the phoneme /d/ in Spanish which are found in COMPLEMENTARY DISTRIBUTION: one allophone, [d], occurs in certain environments (after pause, /n/ and /l/) and the other in all other phonological contexts (in the most widespread standard pronunciation).