While the vaccines might not offer the same level of resistance against the new strains, there's evidence the vaccines are still at least somewhat effective against them.
Let me explain this for some who don't understand it yet:
Immunity is not an absolute. It's a blurred continuum. Generally speaking, with viruses, immunity works by the immune system building antibodies that can connect to the protein spikes of the virus. Those protein spikes are
very complex, which means a sudden flip to a totally different protein build is unlikely. Generally, if a virus gets a mutation in relation to its protein spikes, one
small part of it will change. That will make
some of your antibodies against the virus ineffective, but some will still work. Your body retains some sort of
resistance to the pathogen. 'Resistance' and 'immunity' are not the same things. 'Resistance' implies that something doesn't have
much of an effect on you, while 'immunity' implies that you are completely invulnerable. The reason why you don't die of colds, but you can still get ill from them is because you have
resistance to most of the viruses that cause upper respiratory disease. Part of that resistance is inherited through thousands of generations of coexisting with those viruses, and part of it is through exposure. If you get a cold this year, you will retain some sort of resistance to the virus responsible from the cold you had last year or the year before. Hence, you sometimes get a stuffy nose and a headache (a lot of the time no symptoms at all), but you don't really feel
that ill and you fight it off with relative ease, and your body updates its adaptive immunity to the new mutations the virus gained this year. Rinse and repeat.
COVID doesn't exactly work in that way, but it follows a similar basic model. The new variants will most likely have a small difference in their overall protein structure, but the other 99% is identical to the older variant. Currently we don't think it mutates exceptionally fast, certainly not as much as rhinoviruses, the main culprits of the common cold, so these changes will occur at a considerably slower rate than most other widespread viruses. This means the current vaccines will continue to be effective at preventing
severe disease for quite some time into the future, possibly for the rest of the person's life if they are able to come into contact with new COVID strains regularly and keep updating their adaptive immunity without falling more than mildly ill. When I say 'mildly', I mean getting a headache or a cough for a couple of days, not 'mildly' as in as bad as the flu and just staying out of the hospital. Also, as Lacius points out, the faster we roll out the vaccine to as many people as possible, the more effective it will stay, as less hosts mean less chances of changing its structure in a way that somehow helps the virus to circumvent the vaccine. This is why people not vaccinating their kids for measles and other such illnesses is such a bad thing; right now it's not that common, so most people will stay resistant, but if more and more people start getting it because people aren't vaccinating, the virus will begin to mutate to a point where the MMR isn't effective against it anymore, and a new measles epidemic, and likely pandemic, will ensue, and millions of children and most likely adults too will die, and millions more children will be left permanently deaf. Measles spreads crazy fast: about twice as fast as COVID does, and COVID spreads about twice as fast as regular human upper respiratory infections (RHURI? Can that be a thing now?). Measles is no joke.
Back to the topic at hand, a new variant or 10 isn't the end of the world. The vaccine will likely offer a significant amount of protection against these slightly different variants. 'But muh new variant' isn't a good reason to not take the vaccine, in fact that directly helps the virus to mutate more and worse than diversify, speciate into entirely different species, at which point a single vaccine becomes almost impossible. Don't be an idiot, take your shot.