タクシーの全部{ぜんぶ}が白い{しろい}。
Would that be a natural way to say: all the taxis are white. ?
No, it would not be a natural way to say "all the taxis are white."
You're looking for:
1 タクシーはみんな白い。
2 タクシーは全部白い。
3 タクシーはすべて白い。
4 全部のタクシーが白い。
5 すべてのタクシーが白い。
As was mentioned above タクシーの全部 means "the entirety of the taxi(s)" which requires a very narrow, specific context, although keep in mind that examples 2 and 3 (2 more than 3, though) can also mean "the taxi is entirely white." Lacking grammatical number, Japanese requires extra information/context to clarify part/whole distinctions which are very easy to make in languages like English, which do have grammatical number.
It sounds unnatural to me. If a native speaker hears the sentence, he/she will imagine an unrealistic taxi which is completely white (including body, wheel, sheets, and so on).
Instead, you should say: 「全部のタクシーが白い。」or「タクシーは全部白い。」. But the latter may be ambiguous depending a context, which may again mean "The taxi is completely white.".
"タクシーの全部が白い" There are two meanings.
① "タクシーの全部分が白い" > "All parts of the taxi is white."
② "全てのタクシーが白い" > "All taxis are white."
example
① "私は個人タクシーのドライバーだが、客寄せのための特別な塗装のため、タクシーの全部が白い。"
② "私の所属しているタクシー会社では、保有しているタクシーの全部が白い。"
In general, we use ②.