Depends which animal charities you are talking about. I help run a breed rescue organisation and we try to neuter/spey all dogs before they are rehomed. This is not always possible (too young, too near a season, not strong enough due to medical issues etc etc) and where a dog goes out un-neutered, the new owner has to sign a contract agreeing to neuter the dog themselves within a certain period (the adoption fee is waived if the owner pays for the neutering themselves).
This neutering policy takes up the bulk of our funding - all raised by our own members. Many breed (and general) rescue organisations have similar policies.

I would, however, like to see the RSPCA (with its millions in the bank gaining interest), use some of their money to fund free neutering throughout the country. They should, of course, use the money that is kept centrally and used for dodgy advertising campaigns and not expect their hard-pressed local clinics to pay. At least then the RSPCA could be seen to be doing something positive for dogs in the UK.

__________________
DREAMCATCHER SIBERIAN HUSKIES
Siberian Husky Welfare Association (UK)
"For I am a raindog too!" - Tom Waits
"Believe none of what you hear and half of what you see" - Benjamin Franklin
"As long as people believe in absurdities they will continue to commit atrocities" - Voltaire