What is the meaning of boldfaced lines in the paragraph? [closed]

I think you (and Fraser) have missed an important point: the objectionable thing is not that the men of the North would wish to "make common cause with" the slaveowners, and "put down at the point of the bayonet" any slave rebellion, but that "By the Constitution of the United States...they are bound" to do so, since their "physical power is pledged for [we would say 'to'] the suppression of domestic insurrections". It is therefore the duty of the women of the North either to press for amendment of the Constitution, or to try to abolish slavery altogether. (Bound to' is indeed a (largely British) idiom meaning 'very likely or certain to', but here it clearly has a literal meaning.)

The argument is shaky, though no more so than those of many well-intentioned politicians through the ages. Fortunately, when it became necessary to decide, the domestic rebellion was by, not against, the slaveowners.