What band has had the most members from the start to present day?

My guess would be the wind section of the New York Philharmonic, which today numbers in the 20s.

I don't believe this question can be answered for certain.

The 99 member The United States Marine Band, founded in 1798, with members staying for only 4 years, would certainly have had many members.
https://en.wikipedia.org/wiki/United_States_Marine_Band

Certain college bands, formed later but now number in the hundreds, also of course with a 4-year turnover, might have had more members. Auburn University is one:
https://en.wikipedia.org/wiki/Auburn_university
Spirit of Troy at USC is also huge and has the same turnover ratio:
https://en.wikipedia.org/wiki/Spirit_of_Troy#History

The Dresden Staatskapelle, founded in 1548, might also have had more members. Though officiaally an orchestra, it also might have less turnover even though they've had the early start:
https://en.wikipedia.org/wiki/Dresden_Staatskapelle

Big Bands like Benny Goodman, rock groups like Parliament Funkadelic, Tower of Power etc have had numerous members, though they would be dwarfed by any of the college bands.

As far as rock bands go, the Grateful Dead could hold the record for the number of members.

Jerry Garcia - lead guitar, vocals
Bob Weir - rhythm guitar, vocals
Phil Lesh - bass, vocals
Bill Kreutzmann - drums
Mickey Hart - drums
Ron "Pigpen" McKernan - keyboards, vocals, harmonica, percussion
Tom Constanten - keyboards
Keith Godchaux - keyboards
Donna Jean Godchaux - vocals
Bruce Hornsby - piano, keyboards, vocals
Brent Mydland - keyboards, vocals
Vince Welnick - keyboards, vocals
John Oswald - arranger

https://en.wikipedia.org/wiki/Grayfolded

Grateful Dead has only had 12 members.

Guns N' Roses has had 22 official members.
https://en.wikipedia.org/wiki/List_of_Guns_N%27_Roses_band_members

The Kingsmen have had 23 members:
https://en.wikipedia.org/wiki/The_Kingsmen

Lynyrd Skynyrd has had 25 members:
https://en.wikipedia.org/wiki/List_of_Lynyrd_Skynyrd_band_members

Steppenwolf has had 26:
https://en.wikipedia.org/wiki/List_of_Steppenwolf_band_members

That's the most I could find of any official band. I don't think the person meant bands as in "orchestra's and marching bands" but bands as in "Musical artists from popular music".

Some of you may not consider this an "official" band but Murphys Law (a New York hardcore band) who formed in 1982 & is stll doing shows to this very day has had over 50 members throughout the years.

My thought for the rock band with the most members would be Iron Butterfly. Something like 60 different members since their inception. They have quite the line-up:

https://en.wikipedia.org/wiki/Iron_Butterfly