We had previously said that only Jews “in good standing” may eat of the korban Pesach. The Torah specifically excluded an apostate Jew (one who had left the path of Torah for idolatry), a ger toshav (a non-Jew who keeps the seven Noachide laws) and a sachir (either a hired laborer or a convert who has been circumcised but not yet attended the mikvah). Reviewing these previous exclusions helps to contextualize this mitzvah.
The full verse says, “If a non-Jew converts and offers the Passover sacrifice to God with you, all of his males must be circumcised. When that happens, he will be like any native-born Jew; no uncircumcised male may eat of it.” So, the context is actually one of including the convert – who is now a Jew in good standing – though the “uncircumcised” part applies to any male.
A person might be uncircumcised because he’s not Jewish or, if he is Jewish, because he intentionally spurns the covenant with God. It goes without saying that such a person may not eat from the korban Pesach. But it is also possible that a person is uncircumcised because he had brothers who died from post-surgical complications from their circumcisions. (See Rashi on Talmud Zevachim 15b, s.v. “Arel,” et al.) Even if a person is uncircumcised for this legitimate health concern, he may not eat from the korban Pesach. (All of the people excluded from eating the korban Pesach may still eat matzah and maror on Passover night.)
This mitzvah is #127 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos. It applies at a time when the Temple is standing, but only to men – specifically to uncircumcised men (because circumcision is only relevant to men). The Talmud discusses it in Pesachim 96a and in Yevamos starting on 71a.