Many people who call for Mars to be declared a "nature reserve" aren't just calling for a ban on Mars colonisation, they are calling on a ban on crewed exploration – either of the planet as a whole, or at least of sites they view as "environmentally sensitive" (which basically turns out to be the most interesting exploration targets, and many of the sites which would most easily host crews). They are worried about microbial contamination, which is a rather different environmental concern from Antarctica, and requires much stricter limits on human activity.
When someone like Elon Musk talks about "colonising" Mars, all he's realistically talking about – at first – is a crewed research station, so not that different from what we have in Antarctica. And many people who want Mars to be a "nature reserve" are opposed to even that. Yes, Musk hopes that such a research station will eventually grow into a buzzing metropolis, but I think if that ever happens it is a long way off. Musk might live to see crewed research stations established, I very much doubt he'll live to see genuine colonisation, much as he enjoys publicly fantasising about that topic.
Even the ban on colonising Antarctica only really works because it is banning something no government wants to do anyway. Crewed exploration of Mars would be attractive in principle to governments because of the benefits for national prestige, getting in the history-books, outshining the competition – the same basic reasons why the US went to the Moon. Of course, that benefit has to be weighed against the immense cost – but costs aren't constant, with further technological and economic developments it is going to become more affordable.
All the groundbreaking exploration opportunities with Antarctica have already been used up, so governments don't have the same motivations there. And I think the first human visit to another planet, is going to be much more noteworthy and prestigious and memorable, than whoever was first to explore some big freezing cold island on Earth. A thousand years from now, most people will still probably remember who Neil Armstrong was; I doubt many other people from the 20th century would still be household names (I suppose Einstein and Hitler would be the other likely candidates)–its only been a century or two, but the average person has no clue whom the first explorers of Antarctica were.