The ISS weighs 450 tons and carries 7 people for three months without resupply.
Starship is supposed to carry 14 times as many people for more than twice the duration with one third the mass.
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Have a look at this NASA document Astronaut Mass Balance for Long Duration Missions which lists a 5.74 kg mass balance (in and out) per person per day in Fig. 1. However, in Fig. 2 it shows that 4.53 kg of that or almost 80% is water in various forms.
For 9 months that becomes 1,500kg, for 100 people that's 150 tonnes. That is before adding the 100 humans for 10 tonnes more.
So doing it just by stacking the space full of food, air and water is marginal. However half of this mass is water, so even basic re-cycling equipment to allow water to be recycled two or three times would cut the required mass substantially.
So 100 passengers is not automatically implausible, but does depend a great deal on the details of the life support, and certainly would not be bringing much equipment for use on Mars onboard with them.
Edit: also changing the end result of this math is the possibility that Starship may trade reducing payload to allow higher energy departures to cut transfer times to as low as 80 days. The overall tradeoffs in reducing consumables load to allow quicker transfers are not clear as of 2023.
Starship might be capable of carrying 100 people but that doesn't mean that 100 people is the goal for long term travel.
Interplanetary travel would not be using a mass passenger transport variant of starship, it'd be using a more spacious variant with fewer people. Regardless of mass constraints you'd really not want to be crammed airline style into a restricted space with 100 other people.
The 100 people variant would be used for shorter trips to earth orbit or maybe lunar transfers (though even that might use fewer people).
As mentioned by other answers, Starship may not carry 100 people to Mars; however, it's also worth noting that there are various Starship variants, including crewed and cargo variants. It's very likely that a manned mission to Mars would have some uncrewed cargo Starships to carry all the supplies needed to keep a surface base running; in that case, it would be trivial to use the cargo ships as supply depots for the crewed ships while in interplanetary space.
Edit: to be clear, I'm not saying that this is the best way to transport crew to Mars; it's just one option if you want to put 100 crew in one ship and send them interplanetary.