Tax protestors in Oregon and Idaho submitted petitions yesterday that will apparently place tax-cutting intitiatives like California's proposition 13 on the ballot in both states this fall.

The success of the petition drives in Idaho, one of the nation's most conservative states, and Oregon, which has a rich tradition of liberalism, added to a crazy-quilt pattern of responses to the passage of the California proposition four weeks ago.

Earlier this week, a citizen's group in Michigan said it had enough signatures to force a November referendum on a tax-limiting plan that has been opposed by most political leaders. In Illinois, meanwhile, a similar citizens' initiative sputtered - but politicians pushed a tax relief measure of their own through the state legislature.

The week's events confirmed that "13 Fever" is one of the most contangious political diseases to hit the country in years. But the circumstances were so diverse from state to state that they tended to confound early attempts to come up with simple explanations of the epidemic's causes.

In Idaho, petitions bearing twice the number of signatures necessary to get a Proposition 13-like initiative on the ballot were submitted yesterday, while in Oregon, where 61,646 signatures were necessary, 100,000 were delivered.

California's Proposition 13 rolls back property assessments to 1975 levels and prohibits a property tax greater than 1 percent of assessed value, cutting revenues dramatically.

The state's voters approved the measure by a landslide in the June 6 election despite predictions of disaster from most government leaders. (The proposition officially goes into effect today, and officials have toned down their warning considerably. Because of a massive redistribution of a $5 billion state surplus.)

The landslide vote was followed by an avalanche of analysis from politicians and pundits. Several theories emerged to explain the success of 13.

It was suggested that voters used the huge tax cut to send a message to representatives who were out of touch. Sen. Alan Cranston (D-Calif.) crystallized this view with the observation that Proposition 13 "is like that two-by-four you're supposed to hit a mule with."

Another explanation held that Proposition 13 was an aberration prompted by conditions peculiar to California. President Carter noted that the state had unusually high property tax rates, sharp recent increases in assessments, and a large state budget surplus "Those factors would be unlikely to prevail in other states," the president said.

Some minority group leaders saw the California vote as a racist blow at welfare and other government programs designed to aid the disadvantaged.

This week's developments should complicate such analyses.

In Oregon, the petitions were requesting a ballot line for a proposal identical to Proposition 13, except that it would allow property taxes up to 1.5 percent of assessed value. Generally, 15 percent of the signatures on such proposals are invalidated; thus a vote on the measure seemed assured.

Oregon voters would presumably not need to send their legislators a tax message, because the state already has a tight system of voter control on property tax increases. Any substantial increase in tax rates must be submitted to a popular referendum. Most school districts and many cities have laws requiring annual budget elections even if no increase in tax rates is proposed.

On the other hand, assessments are required by state law to equal fair market value, and inflation has taken a severe toll. In Multnomah County (Portland), assessments jumped 18 percent last year, and some other areas saw even steeper increases.

The Oregon proposal would cut property tax revenues by 42 percent, and that cut would probably cause a dollar-for dollar reduction in government services. Unlike California, Oregon has no budget surplus with which to bail out local governments.

Ray Phillips, a retired boilermaker from Portland who was active in the petition drive, says the voters will not be deterred by the prospective loss of such a large chuck of government revenue. Oregon has no significant welfare expenditures, and there seem to be no other governmental programs that particularly fuel the voters' ire. But Phillips says the public is convinced that the state budget has "plenty of fat."

At almost the same moment the Oregon petitions were being unloaded in Salem, a group of political mavericks gathered for a colorful ceremony outside the Idaho state capitol in Boise to present their own demand for a tax-cutting ballot initiative.

A huge replica of the Liberty Bell rung out three times as Don Chance, president of the Idaho Property Owners' Association, presented petitions bearing 50,000 names calling for a ballot line for the "One Percent Initiative" that is nearly identical to Proposition 13.

The response to the petition drive surprised many state leaders because Idaho seems so far from the California model.

Property tax rates have been moderate, for the most part, and the state government has neither surplus nor deficit. The welfare burden is mild, and bureaucracy at all levels is relatively small.

But Idaho has been undergoing a land boom that has lead to sharp inflation in real estate prices and a resulting leap in property tax assessments. Taxes on a typical Boise home valued a $45,000 in 1977 jumped from $500 to $1,200 between 1977 and 1978 because of the assessment increase.

Such boosts gave the Property Owners Association their initial impetus in January, when they borrowed a copy of Proposition 13 and offered it to Idaho taxpayers.

For months the initiative drive made small progress, but the vote in California provided an enormous spark.Red and white signs urging voters to sign up sprouted in front yards and business offices all over the state.

Idaho's politicians, who initially belittled the initiative, softened their stance as popular sympathy grew. Gov. John Evans, an early opponent, now talks almost like a supporter of the plan, even though the state tax commission has predicted the initiative would cut state property tax revenues by 66 percent.

The California vote had a dramatic impact on tax politics in Illinois, where a once-moribund proposal to cut property taxes through state tax rebates has suddenly become a hot issue in the gubernatorial campaign.

Long before Proposition 13 had passed, a citizens group in Chicago had been pushing for a statewide referendum on property tax relief. But the petition drive never got off the ground.

Two days after the California vote, Michael Bakalis, the Democratic candidate seeking to unseat Republican Gov. James Thompson, announced his backing for a longpending bill in the legislature that would cut local property taxes and use state funds to make up the difference.

The state legislature, which is controlled by Democrats, passed the bill this week to give Bakalis a campaign issue. Thompson must now decide whether to sign the measure, which he has called "fraudulent" and "irresponsible," or to risk the voters' wrath by vetoing it.