My understanding of the blocksize debate is that it would require 51% consensus to change the algorithm and accept the new blocksize.
If the algorithm can be changed like this - would the exact same mechanism allow miners to also change the limit of bitcoin?
Or is there something fundamental that prevents this?
Flat-out increasing the blocksize is a hardfork. Hardforks require the overwhelming support of all parts of the Bitcoin sphere to be adopted, otherwise they will create a forkcoin. 51% would be unlikely to suffice to implement a hardfork.
Changing the reward schedule and thus the Bitcoin supply would also require a hardfork. From a technical perspective, changing the reward schedule would probably require a similar level of changes in Bitcoin software to be rolled out.
However, getting support for a change in the Bitcoin supply would be much more difficult as the fixed supply is a key precept of what Bitcoin is, while the blocksize is "merely" an operational value that has implications for the network's security and how the Bitcoin project develops. I therefore consider it extremely unlikely that the Bitcoin supply will change in the future, while a blocksize increase is almost certain.
I'll give a slightly different perspective than the two existing (great) answers you've already been given, and answer to a comment you made:
Great, but the point is more or the less the same. The idea that 'there will only ever be 21m bitcoin' has the same technical integrity as 'the blocksize will only ever be 1MB'. Whether one is more likely to change or not, is a social issue, not a technical one.
Yes, technically speaking changing the block size is equally hard as changing the total supply or inflation schedule. They both require a hard fork, which means new software needs to be deployed by every network participant, or it will just be a separate currency that forks off.
However, the reason hard forks are hard is because of ecosystem expectations. If participants believe that certain changes are hard, they will be hard. If people believe it to be unlikely that a certain rule will change, they'll need enormous amounts of evidence that indeed every one thinks differently before they'll even consider upgrading to new software that implements this new rule - as they don't want to end up on a separate currency alone (this seems to have been what happened with the B2X fork). If people believe that some group effectively dictates the system's rules, they may just go along regardless (this seems to have been what happened with Ethereum Classic). In my opinion, the ecosystem's assumption that certain changes are hard is the very thing that makes Bitcoin valuable.
So, indeed, it is a social issue if you're talking about highly invasive system changes. But that does not mean every hard fork is equally hard. Ultimately, the system's users define what the system is (which includes miners, but certainly a majority of miners can't arbitrarily decide the rules if it's against the will of the system's users).
My understanding of the blocksize debate is that it would require 51% consensus to change the algorithm and accept the new blocksize.
That is incorrect. Changing the block size would require a hard fork, as it is a change that breaks consensus rules. So if 51% of miners started running code for larger blocks, 100% of nodes would simply ignore their new larger blocks, and continue following the remaining 49% of miners.
The same goes for the supply limit.
In order to change these variables 'cleanly', you need absolute support from the entire community, perhaps most importantly the users running their own nodes. It is perhaps more likely for an attempted change to the consensus rules to result in a chain split, as some % of users switch to the new rules, and the rest remain on the old rules. The game theory involved in these sort of situations is complex, and depends on many variables (what % of users switch, what % of miners switch, if replay protection is implemented, etc)
An important take-away from this is to understand that miners work to validate blocks according to the rules chosen by users. Miners do not decide what rules the users will follow.
