Tensions ran high at the San Jacinto Battleground in La Porte during one such protest.
"We are standing up for human rights and against female genital mutilation and against Sharia law. We are all here to show our support for the U.S. Constitution and for freedom for all people," protester Liz Theiss said as she held a sign purporting to show an injured "Christian girl [who] experienced discrimination."
Across the sidewalk, counter-demonstrators held signs proclaiming "No Trump, No Pence, No KKK" and calling the demonstration a "thinly veiled attack on Muslims."
VIDEO: Houston's Muslim community reacts to nationwide protests
At the Baitus Samee Mosque in northwest Houston, worshipers and members of the community worked to put a dent in some of the misunderstanding at an open house event.
The event was held as the sun went down, signifying the worshipers' breaking of the Ramadan fast for the day.
"Sharia, if you define it, is a path," said mosque member Ata Ahmad, "not something that supersedes the Constitution. It's a way to act to your neighbor, to your children, how to live a nice respectful life."
Hundreds of counter-protesters marched through downtown Seattle, banging drums, cymbals and cowbells behind a large sign saying "Seattle stands with our Muslim neighbors." Participants chanted "No hate, no fear, Muslims are welcome here" on their way to City Hall, where dozens of anti-Shariah protesters rallied.
A phalanx of bicycle police officers kept the sides separated during the sanctioned events, but authorities said a large fight broke out after the gatherings concluded. Police used tear gas to disperse rowdy demonstrators and arrested three people for obstructing law enforcement.
In front of the Trump building in downtown Chicago, about 30 people demonstrated against Islamic law and in favor of President Donald Trump, shouting slogans and holding signs that read "Ban Sharia" and "Sharia abuses women." About twice as many counter-protesters marshaled across the street.
A similar scene played out in a park near a New York courthouse, where counter-protesters sounded air-horns and banged pots and pans in an effort to silence an anti-Shariah rally. In St. Paul, Minnesota, state troopers arrested about a half-dozen people when scuffles broke out at the close of competing demonstrations at the state Capitol.
"The theme of today is drowning out racism," said New York counter-protester Tony Murphy, standing next to demonstrators with colorful earplugs. "The more racists get a platform, the more people get attacked."
The rallies, held in more than two dozen U.S. cities, were organized by ACT for America, which claims Islamic law is incompatible with Western democracy.
The organization said it opposes discrimination and supports the rights of those subject to Shariah. However, the Southern Poverty Law Center, which tracks hate groups, calls it the largest American anti-Muslim group.
"I don't believe Islam can peacefully co-exist with the Constitution," said Seattle anti-Sharia demonstrator Aaron Bassford, 29. "We need unity in this country under no ideology and no banner except the Constitution of the United States of America."
But the overwhelming majority of Muslims don't want to replace U.S. law with Islamic law, known as Shariah, and only "radical extremist groups" would call for that, said Liyakat Takim, a professor of Islamic studies at McMaster University in the Canadian city of Hamilton, Ontario.
Shariah, Takim said, refers to guidelines or principles - how Muslims should live. "Fiqh" refers to jurisprudence, or specific laws. The values embedded in Shariah do not change and are shared among Muslims, he said, while fiqh is open to interpretation and change, and in fact differs among Islamic sects and communities.
"The Quran allows slavery. So does the Old Testament. That doesn't mean we allow it today, too," Takim said. "Laws are amenable to change."
In Seattle, activists set up an "Ask an American Muslim" booth to give rally participants on either side a chance to speak with a Muslim.
"American Muslims support the American values and freedoms we all cherish," said Arsalan Bukhari, executive director of the state chapter of the Council on American-Islamic Relations.
The marches come amid a rise in reports of anti-Muslim incidents in the U.S., including arson attacks and vandalism at mosques, harassment of women wearing Muslim head coverings and bullying of Muslim schoolchildren.
In California, small but raucous demonstrations were held in a handful of cities, including San Bernardino, where a husband and wife inspired by the Islamic State group killed 14 people and wounded 22 in a 2015 shooting attack.
Clusters of protesters and counter-protesters gathered on four corners of an intersection at a memorial to the slain, yelling and waving American flags and posters proclaiming various causes. Anti-Islamic law demonstrators marched past the building where the shootings occurred.
"There's an anti-Trump, a pro-Trump, anti-extremists, so there are a variety of messages here," San Bernardino police spokeswoman Eileen Hards said. "There are so many messages going on that I'm not sure who's who."
Anti-Islamic law protester Denise Zamora, 39, said she and others in her group were not opposed to all Muslims.
"We're anti-Shariah. We're anti-radicals," the Upland woman said. She added, of Shariah: "It's coming in very slowly, and a lot of the refugees are bringing that ideology here. All of it is just barbaric."
About 300 people attended San Bernardino's rallies. Three were arrested on suspicion of vandalism for smashing windows of two cars, Hards said.
The Associated Press contributed to this report.