Quite a few people play golf who are disabled to some extent. .Douglas Bader was one! Most golf clubs have buggy's for those who can't walk very well but still like to be active to the best of their ability.
I think it is you who are missing the point - Blue Badges are not awarded on the basis of disability - they are awarded on the extent of impaired mobility. A person who is very old and can only walk with the aid of a zimmer frame is not classified as "disabled", but they may still qualify for a Blue Badge because they are unable to walk very far. A person can be classified as "disabled" and so get certain benefits but not qualify for a Blue Badge - e.g. my colleague who lost his leg in military service is classified as "disabled" and so gets certain benefits and allowances, but he would not qualify for a Blue Badge (nor does he want one) as he is still very mobile and indeed still runs regularly. Deaf people are also considered "disabled" and are therefore given various benefits - but they don't qualify for a Blue Badge as their mobility is not hindered.
Anybody who is able to play golf (even if going in a buggy between holes) is relatively mobile and fit as they can clearly stand and vigorously swing a club, and so would justifiably not be at the top of the priority list for Blue Badges. Whether they make the cut-off or not I suppose depends on the council's guidelines.