Is "new" acceptable when using C++ objects in a FreeRTOS application?
This isn't about malloc vs new, rather it is about "should you use heap allocation in an embedded system, or not?" which is more of a philosophical question.

Heap memory management is very useful from a programmer's point of view, however in an embedded / real time application, when an allocation fails, you're in trouble.

If all memory is preallocated (ie, statically), then you can prove that the software will never run out of memory. You can't prove it when using dynamic allocation. If you manage memory manually (which is a pain) there can also be memory leaks, double free's, and other fancy bugs. Additionally, since you are using a preemptive multitasking OS, you have to wonder if your memory allocator is thread-safe. If your code uses lots of allocations, overhead may be substantial.

Memory fragmentation is a real problem on long-running systems, too. And this one is quite subtle. You need an allocator designed to mitigate this, but it will only work if the allocations are small enough in size. 

So... it's a tradeoff. You have to think about the details.