How is it that some people take a shower after going into the mikveh Erev Shabbos or Yom Tov, when the Shulchan Aruch says that should not be done?
because there are probably some who argue on the mechaber and are matir for whatever reason.
The Shulchan Aruch speaks of women. Men, who have no actually obligation L’Halacha to go the mikvah may shower after going to the mikvah. R’ Wosner writes this explicitly in Shevet Levi.
There are many who Mattir taking a brief shower as long as the intention is not to get the mikvah water off but some other intention like the mikvah floor is dirty…
Please note that just because you couldnt find a Halacha in the shulchon Aruch doesnt mean it doesnt exist. Did you check the Nosei Keilim as well as other Halachic sources?
As stated above a person has no obligation to go to the Mikva (nowadays) so the Inyan doesn’t apply. Actually according to Kabbalah (Reb Chaim Vital), one should shower after the Mikva.
In the sefer Oleyhu Lo Yibol it is said that Reb Shlomo Zalman Oirbach showered before and after the Mikvah,
When asked why he said.
“I shower before the Mikva because of the Mitzva of VeOhavto LeReyacha Komocho.
I shower after the mikva because of others that are not carefull in the mitzva of VeOhavto LeReyacha Komocho.”
I believe this is an inyan related to women on their leil tevilah. And even in that case, there is a heter for certain women to shower with some type of chatzizah on them, like a bandaid.