Story highlights Roy Moore defeated an incumbent Republican in an Alabama primary Tuesday

His rise has worried Senate members of his own party of primary challengers

(CNN) Roy Moore's victory in the Alabama Senate primary is provoking fears in the halls of the Capitol, with Republicans openly worried that Moore's slash-and-burn politics could have broader implications in 2018 and beyond.

A wide range of Republican lawmakers reacted with alarm Wednesday, saying that they hope Moore will fall in line with the rest of his conference if he wins the special election in December. Otherwise, several said, it could have a broader impact across the party if Republicans are saddled with controversies stemming from Moore's inflammatory rhetoric, particularly on social issues.

"Obviously I'm not enamored with his politics," said Arizona Sen. Jeff Flake, a Republican who could face a tough primary and general election next year. "I don't think that's the future of the Republican Party. That's for sure."

Asked if Moore's views could spell problems for his party, Sen. Richard Shelby, the senior GOP senator from Alabama, said bluntly: "We'll have to see. It depends on where you're running from."

Moore, a former chief justice of the Alabama Supreme Court, came into prominence over his staunchly conservative views on social issues, criticism of homosexuality and belief that the separation of church and state has been interpreted far too broadly. His defiance of a federal order to get rid of a monument to the Ten Commandments at the Alabama Supreme Court prompted his removal of the bench in 2003, the first of two such instances.