Regular employees can choose what company to work for and stick with it. Freelancers meet new clients everyday - repeat businesses, referrals or simply new people. How can you pick and choose, especially when the reason is not quite clear?

For example, I avoid websites with following themes - religious/adult/gambling/alcohol/meat etc. (I'm sure I'm missing some.)

People even get offended/confused about why I'm turning their site down, if it's not blatantly clear (like porn?). Freelancing is greatly based on referrals, and when a client refers me to another client whose line-of-work I cannot approve, I run into embarrassing situation.

For example, this one guy wrote about non-vegetarian recipes. He was like, "I'm not selling any meat! Why can't you take my site?" I don't/can't, because I fall sick. (No, not a coincidence or a hint from universe, probably due to the dilemma eating my brain.)

Telling me things like "None-of-my-business" does not work for me. I tried that over and over.

I contact several new prospects on my own daily (not cold-calling), but sometimes during the middle of the conversation, I realize I cannot work for the company due to their line-of-work, and it leads to a very embarrassing situation.

I also hope you realize that I'm not coming from "holier-than-thou" attitude. I'm sure I'm not better than anybody else ethically or morally, but I don't know what to do about this particular situation.

Question: How to turn down projects without upsetting the client or client's referral and creating an embarrassing situation for everyone involved?