The rabbinic tradition sees them as seminal figures. I am not sure they are any more real than Romulus and Remus.
“teach me the entire Torah while I am standing on one foot.” ~(Shabbat 31a)
One famous account in the Talmud (Shabbat 31a) tells about a gentile who wanted to convert to Judaism. This happened not infrequently, and this individual stated that he would accept Judaism only if a rabbi would teach him the entire Torah while he, the prospective convert, stood on one foot.
First he went to Shammai, who, insulted by this ridiculous request, threw him out of the house. The man did not give up and went to Hillel. This gentle sage accepted the challenge, and said:
"What is hateful to you, do not do to your neighbor. That is the whole Torah; the rest is the explanation of this—go and study it!"
Do not do to others that which angers you when they do it to you." – Isocrates[
It's very simple. The theology of Catholic Christianity, and thus all major forms of Christianity, was constructed fundamentally on the claim that Jesus was a real human being. The fundamental essence of Judaism isn't dependent upon the existence of Shammai.
If Jesus wasn't a real person then the foundational doctrines of 99% of existing forms of Christianity fall apart. So Christianity is existentially dependent upon the historicity of Jesus Christ, which the founders of Catholicism stated themselves. It's why the human existence and birth of Jesus is the primary doctrine of Catholicism.
The post-Mishnaic traditions about Hillel and Shammai are mostly non-historical but there is enough early tradition in the Mishnah to strongly support historicity. (Although the historical Hillel and Shammai were probably substantially different from the Talmudic figures.)
The late second century rabbis debated about what to do when the Passover fell on a Sabbath but they kept details about two obscure figures of the past? I am not convinced the rabbis knew much about anything to do with pre-70 CE Judaism.
There's a reasonable tradition that Gamaliel and the various Gamliel's are descendants of Hillel (perhaps through a son, Simeon/Shimon ben Hillel) but a lot of this seems to be uncertain.
First Generation (10-80 C.E.):
Principal tannaim: the Shammaites (Bet Shammai) and the Hillelites (Bet Hillel), 'Aḳabya b. Mahalaleel, Rabban Gamaliel the Elder, Ḥanina, chief of the priests ("segan ha-kohanim"), Simeon b. Gamaliel [I], and Johanan b. Zakkai.
Second Generation (80-120):
Principal tannaim: Rabban Gamaliel II. (of Jabneh), Zadok, Dosa b. Harkinas, Eliezer b. Jacob, Eliezer b. Hyrcanus, Joshua b. Hananiah, Eleazar b. Azariah, Judah b. Bathyra.
Third Generation (120-140):
Principal tannaim: Ṭarfon, Ishmael, Akiba, Johanan b. Nuri, Jose ha-Gelili, Simeon b. Nanos, Judah b. Baba, and Johanan b. Baroḳa. Several of these flourished in the preceding period.
Fourth Generation: [140-165?]
This generation extended from the death of Akiba (c. 140) to that of the patriarch Simeon b. Gamaliel [II] (c. 165). The teachers belonging to this generation were: Meïr, Judah b. Ilai, Jose b. Ḥalafta, Simeon b. Yoḥai, Eleazar b. Shammua, Johanan ha-Sandalar, Eleazar b. Jacob, Nehemiah, Joshua b. Ḳarḥa, and the above-mentioned Simeon b. Gamaliel [II].