What are the bad consequences of such an action, on a personal level and in general, if there are any?
No, this is not considered to be a sin, because Islamic says
that personal conviction has its role to play in marriage. (A woman may not
like a man because of something in his appearance, and she is not sinning if
she refuses his offer of marriage), but if you fear that you may miss the
boat or that you may not receive a similar offer, then put your feelings
aside, use your common sense and hasten to get married.
From the answer of Shaykh Ibraaheem al-Khudayri.
If a woman follows her whims and desires by rejecting a man
who is religiously-committed and has a good attitude, she may be punished by
remaining a spinster (i.e., unmarried).
May Allaah bless our Prophet Muhammad.