Who even buys mutt-rabbits? Are you planning on keeping all of them?!
I can see the relevance of this. Maybe you think your crosses are cute, and place a high value upon them. What if you are the only one that feels that way? Are you prepared to provide homes for any angora rabbits you can't sell? I've seen hybrids advertised for free by their breeder because they were so desperate to get rid of them. "Free to good home" ads are not a responsible way to find homes for rabbits you no longer wish to keep for yourself. I won't go into that here (if you are curious, just google it!). Most show breeders cull heavily... And not all of their culls find pet/fiber homes... If you don't have the stomach for this, think twice before you put your buck in with your doe!
How will hybrid offspring improve upon the stock you already have?
Think about it. What do you hope to accomplish by crossing angora breeds? Do you have a specific goal in mind? Far be it from me to tell you what your goals should be in breeding angoras, but make sure you have some clear goals in mind. In addition, you need to remain objective in assessing whether or not your choices are helping you to achieve these goals. If you desire a competitive edge on the show table, understand that you will need 3 more carefully bred generations before the offspring of your original outcross will be eligible for ARBA registration. In the case of German hybrids, there are strict expectations for confirmation and wool production that angoras other than purebred Germans have difficulty achieving.
You never quite know what you are going to get!
When you first cross two established angora breeds, the offspring will be a hodge podge of parental characteristics. You have no idea what they will end up looking like, what kind of wool they will produce, what kind of body type they will end up with, how difficult it will be to manage their coats... It's a crap shoot! With established breeds, you can expect the offspring to resemble the parents. Much work has went in to producing this outcome! Are you sure you are apt to deal with the potential variables?
Integrity of purebred lines
Once you start crossing breeds, you are on your own for awhile. There is no outside evaluation of your stock to a standard, because you have left the realm of breed standards! If your goal is to make it back to the SOP, you have your work cut out for you! Much culling will be needed. Not every rabbit has something to add to a purebred line, and very few possess traits that will improve on what already exists!
Confusing those new to angoras
There is no such thing as the "angora rabbit breed". There are the ARBA recognized angora breeds: Satin, French, English and Giant; and the German angoras that have their own registration organization, the IAGARB.
This can be confusing! Only a 100% German angora is considered a "German". No outcross is allowed to make their way back to purebred status in this club. A hybrid line, regardless of percentage, will always be considered crosses/hybrids.
You cannot register anything before the F4 generation of hybrid offspring with the ARBA. This means, your cross will have to be bred back to purebreds for three more generations! Anything other than a purebred 3-generation pedigree should never be considered to be "show quality". Regardless of their adherence to a purebred SOP, they cannot be registered, and any legs won are in effect useless, because they cannot be used towards a Grand Champion title.
That being said, any rabbit can be shown through ARBA. It can be helpful in guiding experienced breeders in improving their stock through outcrossing. But there is a high standard here-- don't label your rabbits as something they are not!
In conclusion, these are YOUR angora rabbits. As long as you take responsibility for bringing them into this world, you have the right to breed as you please. Please take the time to understand the concerns purebred breeders have over breeding and marketing crossbreed and hybrid rabbits. They make some great points!