The difference is because the vowel after the “d” is stressed in incredulity but not in incredulous.
At one point, the letter "u" was pronounced more or less like its name in both words: "yoo" (in the International Phonetic Alphabet, the "y" sound is spelled /j/, so we'd transcribe it /ju/). But the "y" or /j/-sound in English tends not to be stable when it comes after various consonants (among them t, d, s, z, n, l, r). In particular, after a stressed syllable, /tj/ tends to fuse into a "ch" sound (IPA /tʃ/) and /dj/ tends to fuse into a "j"/"dg" sound (IPA /dʒ/). This is called "yod coalescence". So incredulous used to be pronounced like in-cred-you-lus, but this evolved to be more like in-credge-u-lus. Compare the pronunciation of individual or perpetual.
However, that evolution didn't happen as easily when /tj/ or /dj/ came before a stressed vowel sound. In that case, American English speakers tend instead to drop the "y" or /j/ sound and leave the /t/ or /d/ intact. This is called “yod-dropping”. Compare the pronunciation of the words tune, dune, dual: American English speakers tend to pronounce the letter "u" in these words as "oo" /u/ rather than as "yoo" /ju/.
Another similar case is the t in future vs. futurity or perpetual vs perpetuity. People do sometimes use the same consonant sound for both. But often, the second (but not the first) of the words in these two pairs is pronounced with a plain /t/ sound before the following vowel: /ˈfjutʃəɹ, pəɹˈpɛtʃuəl/ (FYOOCH-er, per-PETCH-u-al) vs. /fjuˈtʊɹət̬i, ˌpəɹpəˈtuət̬i/ (fyoo-TURE-i-ty, per-pe-TOO-i-ty).