I heard in a Shiur from Rav Yisroel Reisman quoting the Chasam Sofer (Responsa 101) who suggests two answers. In the second answer, The Chasam, Sofer says that since we say Nishtane Hateva (nature has changed and thus things stated in the Talmud that once did affect a persons health) technically there should be no reason to keep meat and fish separate. He says, according to this, that if a pot was used to cook fish, and thus absorbed its taste, one does not need to kasher the pot in order to use it for meat despite the concern for the danger.
The basis for this answer is that the Chasam Sofer draws attention to the fact that the Rambam omits certain dinim of cooking meat and fish together, which the Gemara took to be dangerous. The Chasam Sofer attributes this to the fact that, according to the Rambam, nature had changed. Nevertheless, we still keep these dinim under the category of minhag.
Based off of this, Rav Reisman suggests that a convert need not keep a separation between meat and fish, as the only reason that we keep such a practice, is because of the minhag, which of course, a convert does not have.
For a fuller treatment of this topic, see here.
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