Not very favorable to the club.  You may be in violation of the Americans With Disabilities Act, which prohibits discrimination against individuals with a disability.  Your liability may depend on whether the U.S. Department of Justice decides your club is legitimately considered a private club not covered by the Act or is a public accommodation subject to its coverage.  DOJ will consider factors such as the degree to which members control club operations, the selectivity of the membership process, the fee schedule, and the extent the facilities are open to the public.  If you are considered a public accommodation, you will probably be required to make a reasonable accommodation for your member.

If you are not liable under the federal law because you are considered a private club, you could still be liable under a similar state law that has broader coverage or a more stringent definition of public accommodation.

Even if you are not legally required to admit the member with the dog, it is hard to believe that you would make a unilateral determination to bar the dog because you “feel it is not safe for the dog,” apparently without having had a serious conversation with the member and a discussion of the dog’s ability to deal with the situation.  Service dogs are usually well trained and have significant abilities that might not be immediately recognized by someone who has no need for their services.  Most organizations that deal with the general public have found ways to accommodate their presence to help serve their customers and clients.  It is hard to believe that you could not do the same, even if not legally required to do so, and would apparently not even be willing to try.

Finally, you could be required to reinstate your member if you didn’t carefully follow your procedures for expulsion or if a court determines that your reasons were arbitrary or contrary to generally accepted standards of procedure.  I can fully understand why a member would say offensive things when denied access to the night club of which he thought he was a member, especially when the rationale seems as arbitrary as your question makes it seem.  I would expect a club of which I was a member to make a greater effort to accommodate my needs so that I could enjoy the basic activity I had signed up for.