Well Gilroy said the same thing so I doubt there's much friction other than some jealousy on the accolades Andor is getting from critics. Filoni can handle the nerd side of Star Wars just fine but he's definitely a Lucas disciple down to his inability to write compelling dialogue. Ahsoka proved that out. Gilroy writes for adults. Filoni writes for the prequel and Clone Wars generation. I think Favreau is too busy to care that much. Gilroy's dismissiveness about not caring to fill the same mythos exactly as they do might rub him the wrong way.
I don't know why they would need to collaborate or communicate since Andor is a bottled in series. It won't have any effects on Ahsoka or Mando other than Mon Mothma making an appearance which she's already done. All of the people from Andor and Rogue One are either dead or their stories ended. I know Gilroy leans on Pablo Hidalgo and the story group for lore and making sure he's not stepping on toes or breaking canon too much. They did completely rewrite the K2SO origin that was in a comic book but who gives a shit. That crap bothers me to begin with.
Adding Mon's Senate speech actually worked well because it was her open rebellion against the Empire warning her colleagues that they're all being played which not as many people saw. Then you can still have her give her Rebels speech because it fits with asking people to join the Rebellion. I know Dan Gilroy was opposed to using Mon's existing speech because he hated it so Tony wrote a new one for the show but they still referenced the Rebels one.
https://www.empireonline.com/tv/news/tony-gilroy-andor-existence-mandalorian-exclusive/