Is it dangerous to use a battery charger with batteries of a different brand?

There is no danger.

No danger if you use rechargeable batteries of the same type/voltage.

Brand doesn’t matter, but chemistry does.

Using a charger for NiCads on NiMH batteries (or vice versa) is moderately bad, and LiPo batteries have their own requirements, but putting Energizer NiMH AAs in a Panasonic NiMH charger is perfectly fine. And LiPo packs are not available in standard sizes like AA so you don’t really need to worry about them unless you want to use, say, a cellphone charger to try recharging your AAs. (LiPo batteries are used in things that generally come with their own special charger anyways; laptops, smartphones, etcetera.)

NiMH cells are good at high-discharge tasks like camera flashes. Trying to draw that sort of power from an alkaline (regular non-rechargeable) battery could make a number of bad things happen, in part because they cannot handle high-draw loads as well and partly because they are 1.5 volts instead of 1.2 volts which could fry thinks that were expecting 20% less voltage than an alkaline battery puts out. Using NiCads instead of NiMH is less problematic, though recharging NiCad cells with a NiMh charger is dicey enough that I would advise against it.

Most rechargeable AA batteries on the market right now are NiMH, including Panasonic Enerloop™, and thus interchangable. Some older/cheaper rechargeables are NiCads though, so it doesn’t hurt to check the packaging.