> There will very obviously not be any kind of Mars "colony" in our lifetimes
Define "Mars colony". A thriving metropolis with millions of residents? Or a permanently crewed research station with a few dozen staff? The former is not going to happen in our lifetimes. The later isn't certain but I think it has some chance of happening. But Musk is going to try to set up the later and call it a "Mars colony", with the declared ambition of eventually developing it into the former. Aspirational naming.
> there are too little resources on Mars, and too harsh conditions, for it to make any kind of sense.
In 2021, Musk has a net worth of $170 billion. He's only 50, he could easily live for another 30 or 40 years. It is entirely plausible that by the time he dies, he will be a multi-trillionaire. To whom, or to what, is he going to leave his trillions? (Heck, forty years from now, quadrillionaires could even be a thing, and old man Musk could be one of them.) He might leave them to a charitable foundation dedicated to paying for the colonisation of Mars. If that happens – well, even if you are right that colonising Mars is pointless, if a multi-trillion, or even multi-quadrillion, dollar foundation is willing to pay for it, it may actually happen, no matter how pointless it may be.
Another possible scenario: sometime in the next few decades, the US successfully lands on Mars, and sets up a modestly sized US-led international research base. The US government continues its policy of excluding China, so China responds by landing on Mars independently and establishing their own competing Mars base. China and the US then become trapped in a new space race, in which each seeks to outdo the other with the size and capabilities of their respective Mars bases, not motivated by any practical economic or military benefits, but simply by national pride and prestige. A US-led Mars base could grow into thousands of people, and US Congress might become politically locked into paying for them out of the federal budget, even if their existence doesn't actually benefit the average US citizen in any tangible way.
(The above two scenarios are not mutually exclusive, it is possible both might happen at the same time.)