The movement to simplify the U.S. tax code has inspired many marriages of convenience among threatened groups, but few as eye-catching as a recent union of Texas oilmen and New York Jewish leaders. Their mission: to protect the oil industry's tax breaks.

"We walk into meetings together, and people's eyes widen," said Marshall Brachman, an independent oil producer from Fort Worth. "At first some people think it's a joke, but by the end of the conversation, they usually say: 'Why didn't I think of this before?' "

This union of influential but unlikely allies grew from the shared desire of supporters of Israel and domestic oil producers to curb U.S. dependence on Arab oil.

The Council for a Secure America, as the new coalition calls itself, is pursuing that goal by trying to save tax breaks that promote domestic oil drilling -- breaks that many would-be tax simplifiers would like to curtail.

"To carry on an independent foreign policy you want to have an energy policy that doesn't put us Americans in a position where we're exposed to blackmail" from foreign producers, said New York businessman Selig Zises, a prominent supporter of Israel, sounding like a Texas oil producer. " . . . We need more incentives, not less, for domestic oil and gas."

The mixed marriage was arranged by Rep. Tony Coelho (D-Calif.), chairman of the Democratic Congressional Campaign Committee, who usually applies his matchmaking to Democratic fund-raising. Coelho pointed out that Jews and independent oil producers historically were among the most generous contributors to Democratic campaigns, although oil producers recently have become more Republican.

The oil import issue, Coelho said, is a way to bring them together. He traveled last year to Israel with a group of Texas oil producers and New York Jewish leaders. Later he hosted a catered kosher dinner at his home attended by House Majority Leader James C. Wright Jr. (D-Tex.); Dallas independent oil producer Frank Pitts; Zises, who heads Integrated Resources Inc., the fourth-largest seller of publicly registered tax shelters in 1984; officials from the Israeli embassy and the American Israel Public Affairs Committee, a pro-Israel lobby, and about 40 others.

The coalition now has offices in New York and Washington, and a Washington lobbyist, Daniel Dutko. It has a budget of $300,000, mainly for "educational trips," such as ferrying northeastern members of Congress to the oil fields and southwestern members of Congress to Israel.

Its 12 board members include Mack Wallace, a member of the Texas Railroad Commission, which regulates the oil industry, and New York attorney Howard Squadron, past president of the American Jewish Congress.

For now, the council is working to defend percentage depletion and intangible drilling write-offs, the two most lucrative tax breaks of the oil industry, worth a total of $6.5 billion in fiscal 1986. Sources said President Reagan has agreed to preserve these in some form in the administration's forthcoming tax proposal.

But the council also aims to win allies in Congress for aid to Israel, decontrol of the price of natural gas and more. In March, it flew four New York Democrats to the Texas oil fields, where they saw oil wells and dry holes, heard that the chances of finding oil are one in 10 and were told that oil producers need tax breaks to drill against those odds.

The results of the trip were mixed. Rep. Charles E. Schumer, an opponent of the oil industry's prime tax breaks, said his views did not change. But Rep. Edolphus Towns said he emerged "a 100 percent supporter." Other travelers included Rep. Thomas J. Downey, a member of the tax-writing House Ways and Means Committee, and Rep. Robert J. Mrazek.

One side effect of the coalition's formation is to demonstrate the ease with which aggrieved groups are making common cause to oppose major tax revision.

Downey, an oil-industry critic who supports tax revision in principle, said he would consider supporting the council's agenda if it joined him in fighting a separate proposal to abolish deductions for state and local income taxes.

"Am I convinced that the oil industry's tax breaks are necessary for the survival of America? No. But they may be necessary to the survival of the state and local tax deduction," he said. In New York state, where local taxes are high, that deduction has become a big issue.

Sources said Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) fears that Coelho's role in building the coalition will paint Democrats as protectors of special interests in this year's tax battle. Others called it a "crass" fund-raising ploy. Coelho denies the charge.

"What's wrong with some small businessmen and some pro-Israel people getting together?" asked a Coelho aide. "Nothing. We can play this holier-than-thou routine until we're in the minority and we'll stay there."

Coelho also has distanced himself from the group's support of oil tax breaks, stressing that he made the match before taxes were on the congressional agenda and is no longer closely involved with it. "Children don't do everything you want once you bring them to earth," Coelho said.

Some council members have a personal stake in tax-revision.

Zises' firm arranged $407 million worth of limited partnerships for real estate, equipment leasing and oil and gas ventures, according to a national shelter research company. These would have been less lucrative without tax breaks for oil and other industries.

However, Zises said he views the council's concerns as the national interest rather than his self-interest.

The unlikely nature of the union between the Texans and Jewish leaders has led to inevitable ribbing. Said council board member Charles Perry of Odessa, Tex.: "My wife kids me all the time. She asks me when I'm going to get a yarmulke."