I think a lot of factors would very seriously come into play here. First of all, it would depend on the relationship you had with the people who were willing to pay for your child. It would also depend on the stipulations (if any) that were agreed upon for the repayment for these things--example, do you pay them back at a later time, in a lump sum or partial payments, do you pay them back in other ways that might not require money. It would also depend upon the things themselves that were being purchased--example, do you allow for frivolous unnecessary things to be purchased that your child doesn't really need and/or do you allow for things to be paid for that might enrich your child and/or possibly help them down the line (ie, extracurricular activities such as dance, a sport, music lessons, etc).
I think once those are determined, it might be a bit easier to figure out where you'd stand and how comfortable you'd be. I know I wouldn't just take anything from anyone. It would VERY sorely depend on the relationship I held with that person, how much I trusted them and that sort of thing. I also would probably want to be able to do something in return for the kindness. If finances were strained for me and I knew I wouldn't be able to pay them back, I'd probably offer up some other service where possible. For example, I'd offer to watch their kids for them whenever they needed or to help them out when they needed to run errands, something along those lines. Of course, I'd probably still try to find a way to slowly pay them back..... but that is my own personal way of doing things. I'd also NEVER allow anyone--not even family--to buy my kids something overly frivolous. Sure, while young toys and such are one thing, but there will come a point that certain things will just be off limits. Period. And no matter how much they whine, that will be that. And it won't always be a matter of finances either. But I'm starting to digress slightly. So, back on topic. I think if I were close enough to the family my child was friends with and they were willing to assist in something that would help enrich my child's life and/or provide them something that could help them down the line with a skill or something that could be useful in college or for a scholarship or something like that, I think I'd strongly consider it after discussing things with them. And yes, I'd have to discuss things with them. Even still though, it would probably be super hard. But ultimately, it would be for my child and I'd have to exhaust all my options and do all I could do first before doing such things. But, if after all of that, I needed the help and it was truly something that would be beneficial to my child, and I trusted the family and was able to get a sense of EVERYTHING after some very serious discussions, I might be able to be persuaded. But boy. It would be tough. But then, I think it would be for a lot of people. However, when it falls to how the life of your child will go and what opportunities your child can have, you will do what's needed to see it done.