How seriously should I take Fulcrum Racing 6DB tubeless tire compatibility warning? I recently purchased a bike with Fulcrum Racing 6DB wheels and Kenda Flintridge tires. They came tubed, and I'd like to convert them to tubeless.
However, in a manual on their site, Fulcrum list that only certain Schwalbe tires are compatible:

Only SCHWALBE tyres of the TUBELESS EASY type for E-Road, Road and
Gravel applications (only the products in the tables on page 6) have
been tested and approved for Tubeless Easy conversion with the Fulcrum
2 Way Fit Ready profile. Any other type of Tubeless and Tubeless Ready
tyre is not allowed.

How serious is this warning practically speaking? I could get different tires, but my current tires are basically new so I'd rather not change them yet. Both tires and wheels fit well when running with an inner tube.
I'll attempt to offer a bit more nuance than the other answers. On road bikes, the downside of a poor tubeless fit is that the tire could burp, i.e. you hit something and the bead comes loose from the rim momentarily, while you're at high speed. Given the high pressures involved, a burp could mean that you lose a lot of pressure instantly. This would mean a loss of control. On a gravel or cyclocross bike, a burp is never a good thing, but you shouldn't lose all your pressure, and moreover you're probably traveling slower and on loose (and softer) terrain. The lower pressures may mean that wider tires are inherently harder to burp as well.
Normally, I'd take a manufacturer compatibility list very seriously. Some examples follow. Note that this paragraph refers to hookless rims, which the OP does not have. Enve tested a wide range of tires on its current hookless rims, and they produced an explicit list, including tires that are specifically not approved, and another list that are specifically recommended for its wheels. Zipp instead says that tires must be compatible with hookless rims, and encourages riders to check with the tire manufacturer. They say that these tire manufacturers explicitly said to them that their tires are compatible with hookless rims. Continental, on the other hand, has explicitly said that the Grand Prix 5000 is not compatible with hookless rims in general, and thus Continental tires appear on Enve's not approved list. Cadex merely has a short list of tires that are known to have failed their testing (NB: they also have transitioned to hookless rims).
However, at least Zipp and Cadex appear to have tested a range of tires. Fulcrum's compatibility information is a lot more terse, and it's unclear if they even tested any manufacturers apart from Schwalbe. (NB: see @gschenk's answer; Campagnolo Germany may have told some German forum posters they only tested with Schwalbe.) Thus, I would assume that more tires than just Schwalbe are tubeless compatible on Fulcrum wheels. The problem is that we don't know which ones might fail. Riders should remember the very considerable downside to a poor tubeless fit on road wheels. Additionally, I personally use tires with latex tubes on the road. They provide similar rolling resistance benefits to tubeless setups, and they are actually more puncture resistant than butyl tubes. They are trickier to mount than butyl tubes and they do require daily inflation, but they enable you to forego the hassle of tubeless initial setup (albeit that's a once and done deal unless you change tires). Because I don't face frequent punctures, I don't see the benefits of changing to tubeless. If the OP does need that puncture protection, then at least Schwalbe is known to make good tires as well.
In contrast, you can sometimes ignore manufacturer compatibility warnings entirely. Campagnolo's (which is Fulcrum's parent company) component instructions frequently warn that mixing and matching with other company components can result in mechanical failures, and possibly even injury or death as a result. That warning is meaningless; I've used third party chains, chain quick links, chainrings, and cranksets, and even a competitor crankset, on a Campagnolo drivetrain. I've exceeded the stated rear derailer capacity for both Shimano and Campagnolo. Fulcrum's tire compatibility warning has to be taken much more seriously than Campagnolo's component compatibility warnings. The issue is that we don't know precisely how much more seriously, and it is difficult for consumers to find out which tires may be incompatible.