Comfort isn't really an issue for a 30-minute ride, as long as the bike fits.
Also, for any given price point, an aluminium bike will have better components than a carbon bike, so will probably be more enjoyable to ride.
For a commuter bike, I'd be much more worried about theft and damage, unless you have somewhere secure to park the bike at work.
If you are worried that aluminium will be too harsh, you're probably wrong
but I'd consider steel instead, rather than carbon.
Or just put wider tyres on it.
I've ridden rigid aluminium hybrids with 28mm tyres and had no comfort issues at all.
Any good bike shop should be happy to let you take a test ride of at least half an hour on any bike you're thinking of buying.
bicycles.stackexchange.com/users/13174/David Richerby
If you are going to be commuting regularly so that you rack up some miles, in different kinds of weather, I think it's better to buy an aluminum frame bike and spend the saved money elsewhere.
Upgrading the seatpost, saddle, and tires will make the bike plenty comfortable.
Money can also be spent on more or better clothing - which will make a big difference in comfort if you are riding in unpleasant weather.
Also, remember the cost of replacing tires, chains and cassettes.
bicycles.stackexchange.com/users/24228/Argenti Apparatus
As others have mentioned, for such short rides comfort will likely not be a major concern in the same way it would for endurance events, "bikepacking", or even racing.
That's not to say you shouldn't consider comfort at all - a bad saddle or bad bike fit
can make things hurt in a hurry.
But these are things that can be easily adjusted to make any one of hundreds of bike models work, and you shouldn't need to optimize your comfort beyond pinning down those basics.
That said, I wanted to address the underlying assumption within your question: that some frame materials are fundamentally "more comfortable" than others.
While it is true that it is generally easier to make some materials feel comfortable, in the end comfort, or whatever performance metric
you choose to focus on, is the result of complex interactions between the materials, the geometry (both rider geometry and tube shapes), and the construction of the frame.
With clever enough, or poor enough, engineering you can make any material feel harsh or compliant, stiff or flimsy, responsive or sluggish.
Ultimately, the best and really only way to determine whether a particular bike will feel good for you is to test ride it.
Here is a good video by GCN on carbon vs aluminium frames
bicycles.stackexchange.com/users/25590/Josh Doebbert
I'd read this before buying Carbon fibre, the conditions and environmental consequences are huge.
See https://polebicycles.com/why-arent-we-going-for-carbon-frames/ Also, if you're doing short commutes, might a cyclocross bike be better, you can fit panniers to some of those which might make it more useful.
bicycles.stackexchange.com/users/37111/James
For a fun rider or daily morning rider/ commuter, considering the price point, I would always consider a good Aluminum alloy frame with good groupset over carbon frame.
For very short commutes, like half an hour, take bike that has storage space and makes you work out a bit (for health reasons)
bicycles.stackexchange.com/users/40094/Manzar Abbas
I recently started a gig and am commuting 30 minutes each way over patchy city streets.
I'm currently riding a steel single-speed.
Here are the things I'm looking forward to in my next street bike, once I've saved up for it: Better fit.
Track geometry and track handlebars aren't great for me.
Better brakes.
This bike has long-reach Tektros, which are pretty spongy.
More than one gear.
Self-explanatory.
Pedals suited to street shoes.
Track pedals aren't great for this; I plan on getting some MKS "easy superiors".
Having a bike that doesn't bounce all over broken pavement would be nice, but that can be achieved in a number of ways.
I'm not planning on getting a carbon bike for street riding.
bicycles.stackexchange.com/users/2152/Adam Rice
There are some things that you need from a good commuter bike: Robustness (so that you don't come late to work too often, and won't need a new frame after an accident) Comfort of posture (so that rides are fun) Efficiency (so that rides are fun and fast) Durability
(the bike should live as long as possible with the least servicing as possible) Carbon frames reduce weight, as are aluminum frames supposed to do, so they have a slight efficiency advantage.
Let me stress, how slight this advantage is: If you weight 70kg, and your bike weights 10kg, 1kg more for a steel frame would increase your total weight by just 1.25%.
However, you don't need to carry that weight, the air in your tires does.
The extra weight means a small increase in rolling resistance, but that is dwarfed by the air resistance anyway.
I'd estimate that 1kg extra weight will not decrease coasting efficiency by more than 0.5%.
The faster you ride, the less efficiency will be lost.
So, is such a tiny increase in efficiency really worth the extra dollars?
I doubt it.
On the other hand, aluminum is more brittle than steel, and carbon fiber is much more brittle than aluminum.
With a carbon fiber frame, every accident might be the last, a hard knock at the wrong place suffices to break a tube.
With a steel frame, you basically need to ride full speed into a car to destroy your frame.
So, this is quite a plus in robustness for steel.
In terms of durability, both aluminum and carbon have the plus that they can't rust.
However, a good paint job will keep a steel frame from rusting for a very long time.
My steel frame has been in heavy use for 15 years, and there's still no rust anywhere.
So, carbon gives a negligible efficiency advantage, but that's more than offset by its brittleness and high price tag.
Use either steel or aluminum for commuting.
bicycles.stackexchange.com/users/36555/cmaster - reinstate monica
I'm planning to use a bike for rather short commutes (max half an hour), will the carbon fiber be noticeably more comfortable than aluminium one?
Is it worth buying carbon fiber road bike for short commutes?
bicycles.stackexchange.com
<frames><carbon>
bicycles.stackexchange.com/questions/53802
bicycles.stackexchange.com/users/37101/synapse
For regular commuters, racking up some miles, in different kinds of weather, an aluminum or steel frame bike is better than carbon and the money saved can be spent on other items.  Upgrading the seatpost, saddle, and tires will make the bike plenty comfortable.  The best solution is to go and try bikes out at a bike shop to see which one feels best. An aluminium or steel bike will have better components than a carbon bike for the same price. A cheaper aluminium or steel bike can be upgraded with more comfortable parts, and will be more forgiving for commuting. On short commutes, different bikes make less of a difference in comfort for riders, while considerations like durability and attractiveness to thieves are more important. If in doubt, test ride any bike you are considering purchasing. 
An aluminium or steel bike will have better components than a carbon bike for the same price. A cheaper aluminium or steel bike can be upgraded with more comfortable parts, and will be more forgiving for commuting. On short commutes, different bikes make less of a difference in comfort for riders, while considerations like durability and attractiveness to thieves are more important. If in doubt, test ride any bike you are considering purchasing.