I have a world where populated by simultaneous hermaphrodites. Which are like human women plus male reproductive organs, penis and testicles. They could father children like human males, and bear children like human female. Their bearing fertility drops in the 30s and they enter menopause as human female.

Technology is at a early iron age level. Society is tribal in nature. Most hermaphrodites marry and raise children as couples. In some couples both partners bear and sire children. In others more attractive (richer, higher in status) partner sires while less attractive (poorer, lower in status) bears children. Lowest members usually don't have partners, and raise their children from extra-maritial wiring. Few elites have several wives.

Testosterone has similar effect as in humans but less pronounced: more muscle mass, more aggression, more body hair, potential for balding, reduced ability to bear.

Hermaphrodites with small chances to sire children (unattractive, poor, low status) sometimes undergo castration. Everything else being the same castrated hermaphrodites are considered more attractive as wives due to more pronounced feminine characteristics. Criminals are often castrated against their will, especially the violent ones to make them less aggressive.

Does it make sense to have inter-tribal warfare under above circumstances?

On one hand hermaphrodite tribes who conquer other tribes could increase their fitness by killing the older enemies and taking the younger members as their wives. On the other hand why should any member make a risk, since they could reproduce anyway.

Yes, war is rarely about reproduction.

The most common historical reasons for war can be grouped into the following categories: Economic Gain, Territorial Gain, Religion, Nationalism, Revenge, Civil War, Revolutionary War, and Defensive (preemptive) War.

As long as one of these factors is strong enough, there could be wars. The society you describe might consider wives either an Economic or Territorial gain, but that doesn't rule out other, non-reproductive, Economic or Territorial forces.

The easiest reason for tribes to go to war in the situation you describes is probably territorial. If one tribe has access to a particularly good iron deposit, other tribes might fight to acquire that territory, and the other tribe defending it.

Of course they will. If the tribe has something that others want, they must be able to protect it. And if other tribes have something they need, they could either trade for it, steal it or loot it.

Fertile land, herds, pastures, hunting grounds, springs, trade routes anything important for tribe livelihood might be something worth fighting for.

Since hermaphrodites lack expendable young males to fight their wars, individuals in their 30's and 40's will most likely play that role. Since they are still strong enough to handle the physical stress, but their fertility decline makes them less valuable for child bearing.

Or they could specialize.

Strapping young girl? Military caste. Go forth, try your best to kill
or be killed. Take risks. Don't breed, as death in childbirth is the
worst shame a warrior can know. If you grow old enough to become a man
then you have an awful lot of experience and can be used to train the
raw recruits, not to mention stud the next generation of warriors into
existence.

Likely to get killed in the first skirmish? Don't worry: There's
always a need for the working caste. Feel free to breed if you want
to, but don't expect any special treatment from the other castes.
You're here to primarily support the other castes, including taking
care of other people's children if required. If you grow old enough to
become a man then bully for you.

Wide hips? Good pedigree? Mother has a history of twins? Breeder
caste. You get food, protection and your pick of the men. You're
likely going to die giving birth, but hey, at least you perpetuated
the species. If you don't die and manage to live long enough to be a
man then clearly you're good at this whole 'giving birth' thing, and
the next generation could use some of your genetic material. Go forth
and multiply.

Maybe even have warrior tribes, who extract tribute from peasant tribes. Those who refuse to pay are vanquished and sold into slavery. Which is good occupation for tribes who practice warfare as part of their life, for example by herding and hunting.