Their interests were mutually incompatible.是什么意思？

Their interests were mutually incompatible.

他们俩的利益相抵触。

their

pron. 他（她，它）们的，在提及性别不详的人时，用以代替 him 或 her；

例句
Their permissiveness toward their children reflects the wild abandon of their own lives.
他们对孩子的放任折射出他们自身生活的放浪形骸。

interests

n. 兴趣( interest的名词复数 )，利益，利息，关注；

例句
Old enemies can become new friends even if all their national interests are not in complete accord.
即使国家利益不尽相同，他们也可以化敌为友。

were

be的过去时复数和第二人称单数形式，有时代替 was,用于条件从句、动词 wish 之后等；

例句
Shops, houses, and vehicles were set ablaze.
店铺、房子和车辆全都陷于火海。

mutually

adv. 互相地，互助，对；

例句
They recently failed to negotiate a mutually acceptable new contract.
他们最近未能谈成一个双方都满意的新合同。

incompatible

adj. 不相容，矛盾，不能同时成立的，（与某物）不匹配，[医]配伍禁忌的；

例句
They feel strongly that their religion is incompatible with the political system...
他们强烈感受到他们的宗教信仰与政治体制不相称。