There are situations in which asking a new person "How many partners have you had?" is just not done. Maybe you and your date are minors stuck in high school, where slut-shaming and virgin-shaming abound. In that situation, it's really just too rude to ask a person a question that -- if answered honestly -- would give you information that could lead to him or her being socially ostracized or worse if it got around.
Or perhaps you're in a situation in which your match has been made for you, and the only way you can convince yourself go through with the arranged marriage is to pretend that your intended is everything you could hope for; in this case, asking challenging questions is probably counter-productive.
But if you can't bring yourself to ask that question because you fear the answer might intimidate you ... well, you probably need to grow up a bit.
If you're an adult who has full control over the types of relationships you pursue, asking a date "How many partners have you had?" is a perfectly legitimate thing to do. It's a chance to find out more about this new person you're thinking of sleeping with or are eyeing as a prospective life partner. When you think about what's potentially at stake -- why wouldn't you want to ask this question? Divorce is expensive. Maybe you shouldn't ask it on the first date, or even the third ... but it should come up sometime.
I view this question as a conversation opener. I'm not looking for someone to blurt out "15!" and then clam up. It's a question that should lead to more questions. How does he or she define "partner", for instance? Does he count someone he hung out with a whole lot all through college and grew very fond of, but just kissed once or twice? What about someone she met at a concert, had the most passionate sex she ever had with, and then never saw again? What about someone he dated casually over the course of a year and had sex with a few times, but she wasn't into him and he wasn't into her and they just drifted apart? What about that 72-hour Vegas marriage?
What's his approach to dating? How does she look at love? How does he handle conflict? How does she treat her lovers? These are all things you can find out when you ask a person about his or her past partners. And it seems to me that learning this about the person you're thinking of entangling yourself with is pretty important.
And the numbers do matter. You might find out that your date has been with far fewer people than you, which isn't a red flag per se, but now you know he or she might have less experience handling relationship conflict, less sexual skill, and greater romantic expectations. Or you might find out that the person has been with a lot of other people, but has had no long-lasting relationships. That might be due to bad luck, or you might be dealing with someone who pursued the wrong kind of partners. Or maybe he or she just isn't interested in the long term. It's worth trying to find out why that is; maybe your relationship with him or her will go differently (and better), but maybe not.
And if you're inclined toward short-term relationships and don't care so much about a partner's emotional constitution, love philosophy and relationship style ... there's the matter of personal health. It's entirely possible for someone who has slept with only one person in his entire life to be infected with herpes or HIV, and it's likewise possible that someone else who has slept with 300 people has a bloodstream pure as the driven snow. But the odds of exposure increase with every lover.
So, a good followup question to "How many partners have you had?" in most every situation is "Have you had a test for STDs recently?"
And if the answer is "No", the next question should be, "Would you be willing to get one?"