Any client which implements SSL 3.0, TLS 1.0 or TLS 1.1 necessarily uses implementations of both MD5 and SHA-1, since both functions are used in the internal mechanism for deriving symmetric keys from the shared secret obtained from the key exchange algorithm (this mechanism is called the PRF). Therefore, it is highly improbable that a client may support RC4-MD5 but not RC4-SHA1 cipher suites. Therefore, removing support for RC4-MD5 should not break anything as long as you keep support for RC4-SHA1.
For BEAST, see this answer. Summary: BEAST may work only on browsers which have gone at least two years without patching, at which point BEAST is the least of their worries; they have much bigger holes wide open. In any case, BEAST is an attack on the client, not on the server. I'd say that BEAST is now moot (an interesting application of a known cryptographic vulnerability, but not a real threat nowadays). You usually need to "do something" about BEAST not to improve security, but to appease some auditors who believe that check-lists can replace thinking when applied to technology that they do not understand.
For CRIME, cipher suite is (mostly) irrelevant. You "fix" CRIME by not using TLS-level compression. Existing browsers don't support it anyway (they never have, or they stopped doing it some time ago).