Q: Can the California governor appoint a non-resident as Senator?
Yes, as long as that person becomes a resident before the appointment.
Q: Can Butler take office if she is no longer a California resident?
Butler cannot take office until becoming a resident, being appointed, and presenting the appointment letter to the Senate.
The qualification is not so much residency as inhabitancy.
Apparently, Butler owns a house in California and had lived there for several years before accepting the position in Maryland.1 Butler appears to meet the inhabitancy requirement; but the determination, if challenged, will be made by the Senate.
Article I, Section 3, Clause 3:
No Person shall be a Senator who shall not have attained to the Age of thirty Years, and been nine Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State for which he shall be chosen.
9 The Framers adopted the term inhabitant in favor of resident because, as understood at that time, inhabitant would not, in the words of James Madison, exclude persons absent occasionally for a considerable time on public or private business. 2 The Records of the Federal Convention of 1787, at 217 (Max Farrand ed., 1911).
California does have a three-year residency requirement for the state legislature, but Congressional elections (and appointments) fall under the US Constitution.
Though the following discusses elections, it could also apply to temporary appointments.
Qualifications of Members of Congress, January 15, 2015, Congressional Research Report.
Additional Qualifications Found Prohibited
Durational Residency Requirements
Although debated during the Federal Convention of 1787, there was no “durational” residency requirement included in the Constitution for congressional office, as the qualifications provisions merely provide that one be an “inhabitant” of the state “when elected.” Therefore, even if a particular state law or state constitutional provision provided, for example, that one must be a “qualified elector” of the state as a qualification to hold a particular office, and that to be such a “qualified elector” one must have resided in the state for a particular amount of time, such provision would have force and effect only as to state and local offices, and could not disqualify one from being chosen as a U.S. Senator or Representative. In the Senate election case of Pierre Salinger in 1964, some Senators argued that he was not qualified to be chosen to fill the unexpired term of a Senator from California because, under the laws of the state of California, he had not resided in California long enough to meet the state’s qualifications of being an “elector,” which state law expressly required for a candidate for Congress. The Senate found, in accordance with the findings of the Privileges and Elections Subcommittee of the Committee on Rules, however, that state law cannot bind the Senate in determining the constitutional qualifications for office, and cannot, therefore, add a “durational” residency requirement to the qualification for Senator set out in the Constitution—an “inhabitant” of the state “when elected.”
Federal courts have also found that states may not add to the qualifications of those to be chosen to federal office by establishing durational residency requirements of various lengths as a qualification to be on the ballot or to be elected, and have overturned such provisions of state law when challenged. Similarly, a federal court has found that a congressional candidate is not “disqualified” merely because that candidate has changed his lawful residence to another state sometime before the date of election because, as there is no durational residency requirement for Congress, that candidate could merely move back to the state and re-establish residency at any time prior to the election and thus qualify as an “inhabitant” of the state “when elected.”
1 Is Sen.-to-be Butler Eligible to Represent California?.