2000 Escort ZX2(mazda transmission), 2003 Mach1(same tranny as 99-01 Gt/Cobra/Bullitt), and the 2019 Bullitt, all are more notchy when cold. I take that up to the fluid needing to warm up a bit.
Notchy is relative. Ford has come a long way with the MT-82 transmission. I had a 2012 Boss 302 and when it was cold 2nd became so notchy that it became difficult to get into gear. When it was below 40 degrees out I would just skip 2nd gear until it warmed up.
So far the Bullitt's transmission has been quite smooth in comparison. I can tell when it's cold but it still goes into every gear easily. Even when its cold it shifts smoother than the Boss ever did.
"Crunchy" Gear shifts were never a big concern, just the slipping shuddering feeling on startup. As it turns out I think a big part of it was tires. I got some all seasons on there to get me through the rest of this winter and it vastly improved the experience while cold.
Drain the factory fluid and get Synchromesh.... it’s been discussed on this site (and many other automotive forums) as being the “fix” to notchy manual transmissions: