Before diving into the main question, I need to emphasize a scientific point which is important: masks are effective when well made and used correctly.
Here are some ineffective masks and mask-use methods:
I am 75 years old and have been living in this state 67 years, I must have my smoke, and I’m not going to give up my tobacco for a cheesecloth muzzle!
-- E. Piercy, Los Angeles' Evening Express
I'll get back to this, but as you might guess, all of them were actual things during the 1918 Epidemic.
Dr. McBride Wednesday emphasized the fact that masks should be sterilized at least once every 24 hours. Otherwise they are more apt to become germ carriers than preventatives. Boil your mask for five minutes in water to sterilize it.
-- From The Seattle Star, 30 Oct 1918.
So, for your main question: yes, there were people against masks. Complaints include
the look: the masks "look foolish"; in a debate on a Portland ordinance to require mask-wearing an official said "under no circumstances will I be muzzled like a hydrophobic dog."
the legality: there were numerous claims any legal requirements did not hold and were "unconstitutional"; in cases where there was no law or ordinance, that was sometimes pointed out as the sole reason for not wearing a mask
(Side note with Canada: they had almost no ordinances except one in Alberta regarding railway passengers, which was very loosely enforced to the point where "the approved method of wearing a mask" was to leave it under one's chin "until a policeman appears".)
religious: Christian Scientists (who avoid medicine in general) were among those protesting mask mandates (a pastor who was there later said all that was needed to stop disease was "to close the door of thought against it"); a "young girl" mentioned in a Denver paper said "I believe there is a higher power than the city authorities of Denver who is looking after my health"
the weird: an interview in the same Denver paper explained "my nose went to sleep"
There were communities that certainly took to masks without protests, with estimates of compliance in some towns as high as 95%, but all laws were ad-hoc applied to towns only so there was very little consistency.
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San Francisco was one of those towns that initially started without much protest: when the first wave hit San Francisco in October 1918, and there was a mandatory mask ordinance (pushed through by Dr Hassler, Head of Public Health for San Francisco) and closing of various businesses, there was strong compliance and the drug stores quickly were sold out of gauze. In November 13 there were only six new case reported, leading the Board of Health to re-open theaters and "places of amusement" with a mask ordinance still in effect. The masks were then dropped on November 21 to great celebration as a whistle sounded at noon as people ended their (as the San Francisco Chronicle described) "muzzled misery" and thousands ripped off their masks, with the newspaper cheerfully noting the flu was "virtually over".
In that November 23 week, San Francisco reported 164 new cases; by the first week of Decemember, 722 cases. The Flu was not over.
Soon after the ordinance was re-established in January, this time there was strong protest, and the formation of an Anti-Mask Committee, with a President, Secretary, Treasure, and Vice-Presidents, intended to protest the "insanitary and useless mask". However, the committee's first meeting -- intended to call for the dismissal of Dr Hassler -- fell apart as people shouted at each other and the person renting the hall turned off the lights.
In addition to "grassroots" protest, there was also pressure from the Chamber of Commerce and Merchants' Association; the ordinance was repealed February 1 and that marked the end of (very short lived) Anti-Mask Committee.
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The last reason for protest, which I've already hinted at about with SF story, is the straightforward argument that the masks mandates were scientifically ineffective. There were debates comparing cities with and without ordinances (Chicago essentially skipped having one, for instance) where they had similar infection rates. It wasn't even necessarily a wrong argument:
One difficulty in the use of the face mask is the failure of cooperation on the part of the public. When, in pneumonia and influence wards, it has been nearly impossible to force the orderlies or even some of the physicians and nurses to wear their masks as prescribed, it is difficult to see how a general measure of this nature could be enforced in the community at large.
-- Vaughan, W. T. (1921). Influenza: an epidemiologic study (No. 1). American journal of hygiene.
Later in the same study: "It is safe to say that the face mask as used was a failure."
The state of the world in 1918 wasn't up for producing enough masks against influenza, as gauze, used up for WW1, was in short supply, so people improvised, typically in ways that didn't work. Also, the general scientific consensus ended up being that the 1918-era masks were effective for protecting others from infected people but not protecting the user from getting infected by others, but this was uncertain until after the pandemic, and certainly not a subtlety understood by the general public, who really wanted to get back to their chewing tobacco.
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Cohn Jr, S. K. (2018). Epidemics: Hate and Compassion from the Plague of Athens to AIDS. Oxford University Press.
Dolan, B. (2020). Unmasking History: Who Was Behind the Anti-Mask League Protests During the 1918 Influenza Epidemic in San Francisco? Perspectives in Medical Humanities, 5(19).
“Flu Masks Failed In 1918, But We Need Them Now," Health Affairs Blog, May 12, 2020. DOI: 10.1377/hblog20200508.769108