The reason given for not eating fish and meat together is due to Sakana. In current times it does not seem to be a Sakana, (Nishtanu HaTeva). Would you be allowed to eat them together? If not - why not / If yes - why yes?
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See the discussion here. The Magen Avraham shrugs his shoulders as to why this prohibition became carved-in-stone halacha, but once it did, we accept it as such.
Dose of Halacha brings some sources for this debate and points out interestingly that while it is mentioned in the Shulchan Aruch, there is no mention of this in Rambam: