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?
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:
The Mishna Berura (173:3) and Aruch Hashulchan (YD 116:10) quote the Magen Avraham (OC 173:1) who writes that this is one of many natural phenomena mentioned in the Gemara that no longer apply. The Chasam Sofer (YD 101) suggests that this may be why there is no mention of this in Rambam.
Nonetheless, the Chasam Sofer concedes with the majority of poskim (Chochmas Adam 68:1; Maharam Shick YD 244; Kaf Hachaim OC 173:9), who write that this prohibition still applies even if we don’t understand the danger (See Yad Ephraim 116:3).