united-states
Lack of clarity about the right way to quantify this makes the question rather vague.
I am also limiting my answer to the United States because that is the part of the question that I am able to answer meaningfully.
I don't know what stances were taken by major political parties in other countries although I suspect that the conservative and liberal divide was similar. The grass roots opposition to the war was much greater and the military action was much more controversial than it was in the U.S. in many other countries, but my knowledge of the opposition to the Gulf War outside the U.S. pretty much ends there.
Congressional Action
The most obvious way to quantify that is by the Congressional vote authorizing the Gulf War.
In the U.S. Senate, the vote to commence the war in 1991 was 52-47 with Democrats opposing it 10-45 and Republicans supporting it 42-2. The measure was co-sponsored by 29 Republicans and 5 Democrats in the Senate. But, it was voted upon on the merits rather than opposed with a filibuster that the Democratic majority could have imposed.
In the U.S. House, the vote to commence the war in 1991 passed 250 to 183 (per the link above):
Democrats: 86–179. 86 (32%) of 267 Democrats voted for the resolution.
Mervyn M. Dymally and Mo Udall were ill and did not vote, but would
have voted against the resolution.
Republicans: 164–3. Reps. Silvio Conte, Connie Morella, Frank Riggs
voted against the resolution. Independent: 0–1. Rep. Bernie Sanders
(I) voted against the resolution.
The Democratic party controlled House Rules Committee could likewise have prevented the matter from coming to a vote but ultimately declined to exercise its authority to do so.
The bottom line was that while the measure to Congressionally authorize the war had bipartisan support, it was opposed by a majority of Democrats and supported by almost all Republicans. But, it was not opposed so strongly the the Democratic party that controlled both houses of Congress was willing to deny the President's request to bring the matter to vote on the merits.
The buzz lines that I recall among the opponents of the Gulf War were that the U.S. shouldn't go to war for oil and "Why should we care if a slave holding monarchy that only survives due to oil money is invaded?"
(For what it is worth, I was a very junior Congressional aide for a Democratic member of Congress when the vote was held and worked on the issue in that capacity.)
Grass Roots Action In The United States
Because of the size of the Iraqi army, the preparations for the allied
campaign also took a fairly long time, amassing thousands of planes
and tanks etc.
So, during this time, how strong was the Western pacifist
organizations' campaign in preventing the armed liberation of Kuwait
(and arguing for negotiations or something like that instead)? Where
there numerous but small mass demonstrations, or large ones, etc. by
Western pacifist organization against the planned (and
long-/well-advertised) counter-offensive? Di[d] [even] some political
parties in some Western countries oppose Western military action in
that case?
The grass roots opposition to the Gulf War was largely ineffectual. I do not recall any really major mass demonstrations in opposition to it. Opposition to the Gulf War was headed by by groups such as the Quakers and other "peace churches" which oppose every war as a matter of principle no matter what, and not terribly enthusiastically even by them compared to most other wars.
This site (admittedly not neutral) recounts protests and strikes around the world with the U.S. protests mostly taking place after the January 14, 1991 passage of the authorization to use military force rather than when it was being considered in Congress. Most of the strikes and protests were outside the U.S. but according to that source, in the United States:
Thing hotted up as the threat of war became reality on 16 January.
100,000 marched in San Francisco; in the same city 1,000 people were
arrested in a single day of protests. In Washington, 250,000 marched.
Bank windows were bricked and a fence torn down outside the FBI
building. In Los Angeles, blood and oil was poured on the steps of a
federal building.
(The Baltimore Sun acknowledges these post-AUMF protests but estimates that there were 30,000 people at the San Francisco protest mentioned above and 75,000 at the Washington D.C. protest mentioned above - a number that is particularly credible because the D.C. police have made estimating crowd sizes in D.C. into something of a science.)
A spontaneous demo in San Francisco blocked the Golden Gate Bridge.
Police cars were set on fire and a TV station disrupted. In Chicago
roads were blocked for four hours. . . .
AIDS direct action group ACT UP staged a "Day of Desperation" in New
York on January 23. Protestors forced the CBS national evening news
off the air when they invaded the set shouting "Fight AIDS, not
Arabs". 500 activists shut down Grand Central Station for an hour
during the evening rush hour, floating a large banner reading "Money
for AIDS not war" to the ceiling with
helium-filled balloons. . . .
The protests in the United States that this source describes prior to the war authorization in Congress were much more modest:
The BP refinery in Marcus Hook, Pennsylvania was picketed, as was the
Chevron Oil HQ in San Francisco (28/8/90)....
Financial interests were also targeted. In October 1990, 350 took part
in a demonstration in San Francisco's financial district. Called to
protest against the "destruction of the planet and its people by the
corporate and financial cartels" it focused on corporate links with
the Gulf War. The world headquarters of Chevron Oil were blockaded,
and a US and Chevron flag burned. Traffic was blocked in Market Street
(San Francisco's main street). . . .
in the Coalition forces there was no mass resistance of this kind, but
there was significant opposition to the war. By the end of November
over 50 US service people or reservists had declared their refusal to
go. In New York, the War Resisters League had received more than 400
phone calls from soldiers, including 12 members of one company of 150
Marine reservists. Paul Dotson, a US Marine Corps reservist stated: "I
emphatically refuse to kill for oil in the Persian Gulf".
The US army issued new regulations preventing soldiers from filing for
conscientious objector status until they were in Saudi Arabia. Some
soldiers tried other ways of avoiding the front: there were reports of
300 cases of self-mutilation among US troops in Germany who didn't
want to go to the Gulf.
US Marine Jeff Patterson sat down on the runway in Hawaii and refused
to board the plane due to take him to the Gulf saying that he refused
to fight for "American profits and cheap oil".
According to the Los Angeles Times in a story published on October 21, 1990 (before the AUMF vote) there were a series of protests then with the largest involving 4,000 people who gathered in New York City, another notable one in D.C. attracting 200 demonstrators across from the White House (matched by pro-war counterprotestors whom the police kept separate from them) and 200 people at a rally in Boston. The L.A. times also reported that:
Protest rallies also were held in San Francisco, San Diego and Los
Angeles, as well as in Atlanta, Boston, Chicago, Honolulu,
Albuquerque, Birmingham, Houston, Minneapolis, Portland, Seattle and
Olympia, Wash.
The Los Angeles rally drew at least 400 people to Leimert Park, where
they sang peace songs and listened to fiery speeches.
According to the story a speaker to the 200 people at a rally in Cleveland that day summed up his message as follows:
“There is no reason for this country to be involved in that war,” said
Jerry Gordon of the Committee Against the U.S. War in the Persian
Gulf.
“It’s for big oil and profits and control of the oil interests in
Kuwait and to restore the emir, a dictator, to his throne in Kuwait,”
Gordon said. “We say let the people of that region determine their own
destiny.”
Barbara Epstein in 1992 published a more scholarly treatment of the Gulf War anti-war movement (closed access). The open access teaser to the article in the journal Social Justice notes that:
I didn't recall the protests seeming all that notable at the time from my position in the Capitol, but I don't claim perfect recall of those events either.
There was more liberal elite opposition to the Gulf War than there was grass roots opposition to it, and that opposition largely dissolved when the war itself unexpectedly turned out to be a cake walk.
