American nukes in the UK aren't missiles that can be launched, they are gravity bombs that are loaded onto fighter bombers and would be used tactically as part of a European ground war. This type, to be precise:
https://en.wikipedia.org/wiki/B61nuclearbomb
This is not a first strike weapon nor one that can be used immediately if e.g. Russian ICBMs were to be detected en route to the UK or any other NATO country.
The presence of these weapons in the UK serves several purposes: They are part of the overall nuclear deterrent, but they are also an expression of American commitment to their European allies. It's a signal to Russia that if a European NATO member were to be attacked, they have the ability to deploy this weapon on the battlefield. It's not just theoretical: A total war started by Russia against NATO is unfortunately increasingly likely in the coming years, so one reason this weapon is being transferred to the UK is that there is the expectation that it might be needed soon.
Note that the UK is not the only European nation where American nuclear weapons are present. There are five NATO member states - Belgium, Germany, Italy, The Netherlands and Turkey - that have an agreement with the US enabling pilots from these countries to deploy American nuclear bombs in case of a war, about 20 of the same B61 type mentioned above. These nations are all threatened by Russian nukes, but have no active nuclear weapons programs of their own, so this is a vital part of their deterrent.
All of these nations, with the exception of Turkey, just recently purchased F-35 jets specifically for this mission, replacing older Tornado jets that had previously fulfilled this role. The bombs are under the full control of American officers until the American President and the heads of the respective nations' governments have both signed off their use. The US President approves and permits American officers to unlock the weapons. The local head of government has the final word and full control over their use from that point on.
The point of these protests is that the aid is just as if not more likely to benefit terrorists and enable them to hold out for longer than it is to reach civilians, which in turn makes it possible for these terrorists to continue their holding of hostages. There is ample evidence of Hamas stealing aid from the people who need it, including by force.
Also, stopping these protesters from blocking the crossing would be the task of the police, not the military, but I suspect that you know that and were just looking for cheap polemics.