Well, I don’t really feel that there is something exceptional about the starting tone of this poem. But, I guess, the overall tone of the poem ‘If Thou Must Love Me’ is demanding, disapproving and protesting. 
 
Let me explain. Elizabeth here demands sincere and unconditional love, that is somewhat difficult, uncommon and unrealistic, if not impossible. She also expresses her disapproval of and protest against the typical conditional ‘love’ which she does not believe to be love at all.