Judging by the responses here, the moral of the story is, "You can't be sure how anyone else will react, to anything." With all myriad ways people judge others (and seek to make them insecure), I suspect you have several traits that are much more likely to hurt your prospects and relationships than a cracked screen ever could.
For a job interview? I don't think anyone asks to see your cell phone in the course of an interview, unless, perhaps, the phone is a condition of employment, "Successful applicant must have iPhone 4 or above, in good physical and working condition, current version of iOS installed." Even Apple doesn't ask for that.
More important? Put the ringer on silent, put it in Do Not Disturb, turn the bloody thing off altogether... interruptions are way more likely to sink your ship. If you have to take it out to set an appointment? As long as the screen is facing you, it's unlikely the interviewer will catch a glimpse.
Now, being insecure/self-conscious is rarely a plus in an new situation. So... if that cracked screen embarrasses you? Fix it.
But bottom line? DON'T CUT YOUR FINGERS! Is it likely you're going to badly injure yourself? Who knows. But the cost of an emergency room visit could well be more costly than a new screen.