Let me preface this by asking that you kindly correct any misinformation I may be working with in my question, or further elaborate where necessary.
Rav Ovadia Yosef's psak (ruling) that the returning Ethiopians can be married and need not have any conversion, returned them to their status after more than a thousand years. (This time could maybe be viewed as less of a gap since it was based on Radbaz's opinion that was issued hundreds of years ago, so it is as if they are returning to their status after only hundreds of years of uncertainty). Why is it then that for the case of the anoosim, who have a similar situation in attempting to return (as it may be argued, even in a shorter span of a verifiable gap in their status, and a more close, or at least traceable link) require at least giyyur l'humra as ruled by Rav Mordechai Eliyahu? Where does this difference arise from in their rulings? Couldn't the ruling for anoosim have similarly drawn upon a 17th or 16th century posek like Rav Duran, who was ruling that returning anoosim should be welcomed back without test?
For the benefit of the readership, allow me to clarify the meaning of your question a bit. R' Ovadiah Yosef ruled (for example, in Yabia Omer Vol. 8, Section E"H #11) that the Ethiopian Beta Israel community was Jewish according to halacha and, therefore, required no formal conversion to join the mainstream of the Jewish people. Anussim, or people of Jewish descent whose ancestors converted to other religions under duress and have rediscovered their roots, are only accepted into the community after a process of conversion in order to make sure that they are Jewish. Your question is why we don't apply the same standards to both cases and allow Anussim to reenter the Jewish fold without undergoing a conversion.
In order to understand the answer, we must consider a key difference in the Jewish identities of the Ethiopians and the Anussim, respectively. The reason why the Ethiopian Jews lost their connection with the Jewish people for so long was, according to the theory accepted by R' Yosef, simply a result of their physical isolation from us. The Ethiopians never lost their own sense of identity and never intermarried with the surrounding peoples, but they had no contact with other Jews outside of their community. Thus, assuming that their Jewish status was authentic to begin with - a premise that R' Yosef and many other Gedolim have accepted - there is no reason to cast doubt on it now. The fact that they were separated from the rest of world Jewry for several centuries or even millenia does not take away from their Jewishness.
Modern Anussim, on the other hand, have typically identified as Catholics for several generations. Remarkably, their families frequently maintained unusual traditions that are not characteristically Catholic, such as soaking and salting meat before cooking it, not eating pork, not going to church, or lighting candles on Friday night - customs that they now realize are based upon an historical connection to Judaism. Meanwhile, though, the parents, grandparents and great grandparents of many of these Anussim may have intermarried with other Catholics, making it difficult for us, in retrospect, to determine whether their children were halachically Jewish or not. Remember that we receive our status as Jews from our mothers, not our fathers, and our mothers were Jewish because of their mothers, and so on. So there must be an unbroken chain of Jewishness on the maternal side of our families for us to be considered halachically Jewish. Thus, for a member of one of the families of Anussim to be accepted as Jewish nowadays, we would need to have proof that none of the individual's male ancestors on his or her mother's side ever married a non-Jewish woman, so that his or her mother, maternal grandmother, etc., were all Jewish. Understandably, proving this is close to impossible in the majority of cases. As a result, we require the Anussim to go through a conversion process to ensure that their Jewish identity is established beyond any doubt.
In your question, you mentioned how several illustrious rabbis in the 16th and 17th centuries wrote responsa in which they advocated accepting Anussim without any problem, i.e., without any process of conversion whatsoever. However, the situations to which those rabbis referred were different from the Anussim cases of today. In the circumstances they were discussing, the very same people who converted to Catholicism - not their descendants - are now returning to Judaism. We are not faced with the complexities of their Jewish ancestry; we know that they are Jewish, but they have defected, at least temporarily, from their religion. The rabbis argued that, despite the fact that these individuals were wrong to have converted to Catholicism, we should still accept them now that they have repented and wish to rededicate themselves to Jewish tradition. Had the same rabbis been dealing with the great-great-great-grandchildren of Anussim who reemerged from complete assimilation in the Catholic community centuries later, their rulings would have been much different.
In summary, it is not the quantity of time that has passed since a person's separation from the Jewish people that is the decisive factor in these rulings. It is true that, the further back in history we must go to establish an individual's Jewish identity, the more difficult it is to ascertain the facts about his or her heritage, whether his or her ancestors intermarried, etc. However, in cases where extensive historical research is not necessary because of the presence of other evidence, these conclusions can be made more easily and definitively. Thus, isolated Jewish communities who have maintained an identity that is distinct from any neighboring gentiles but have lived apart from the mainstream of Jews for many generations may be accepted as halachically Jewish without conversion. Since they have not intermarried with non-Jews, we need not suspect any 'dilution' of Jewish status among them - thorough background checks are not required. By contrast, the Anussim of today are the descendants of converts to Catholicism who had completely lost any conscious identification with Judaism and may have affected the Jewish status of their children by intermarrying with other Catholics. Since developing an accurate picture of their personal histories is overwhelmingly difficult, we cannot avoid having questions about their Jewishness. Thus, the contemporary Anussim must undergo what is called 'giyur l'humra', a process of conversion to resolve the doubt that surrounds their Jewish heritage. Finally, Jews whose Jewish identity is well established but who have converted to other religions under duress may, after they have renounced their conversions, be reinstituted in the Jewish community without compunction.