The Russian, who won her third world title Tuesday in front of a boisterous home crowd, came out in favor of the law which has drawn sharp criticism and led Western activists to call for a boycott of next year's Winter Olympics in the Russian resort of Sochi.
"If we allow to promote and do all this stuff on the street, we are very afraid about our nation because we consider ourselves like normal, standard people," Isinbayeva, a two-time Olympic champion, said in English. "We just live with boys with woman, woman with boys.
"Everything must be fine. It comes from history. We never had any problems, these problems in Russia, and we don't want to have any in the future."
At least two Swedish athletes competed Thursday with their fingernails painted in rainbow colors at Luzhniki Stadium, the venue that also hosted the 1980 Moscow Olympics.
Emma Green Tregaro, who won a bronze medal at the 2005 worlds, posted a picture of her fingers on the social media site Instagram, saying "Nails painted in the colors of the rainbow." She followed that with several hashtags, including "#pride" and "#moscow2013."
"The first thing that happened when I came to Moscow and pulled my curtains aside was that I saw the rainbow and that felt a little ironic," Green Tregaro said in a video posted on the website of Swedish newspaper Expressen. "Then I had a suggestion from a friend on Instagram that maybe I could paint my nails in the colors of the rainbow and that felt like a simple, small thing that maybe could trigger some thoughts."
Swedish sprinter Moa Hjelmer ran in the 200-meter heats with nails painted in the rainbow colors.
"Some teammates have done the same," Sweden team spokesman Fredrik Trahn said. "The federation has not discussed it. It is all up to the athletes."
The IAAF, the sport's governing body, said both opinions should be respected.
"The IAAF constitution underlines our commitment to principle of nondiscrimination in terms of religious, political or sexual orientation," IAAF spokesman Nick Davies told The Associated Press. "Allied to this is our belief in free expression as a basic human right, which means we must respect the opinions of both Green Tregaro and Isinbayeva."
Isinbayeva said it was wrong for the Swedes to make such a statement while competing in Russia.
"It's unrespectful to our country. It's unrespectful to our citizens because we are Russians. Maybe we are different from European people and other people from different lands," Isinbayeva told reporters. "We have our home and everyone has to respect (it). When we arrive to different countries, we try to follow their rules."
Isinbayeva has set 28 world records in her career and won seven major titles, including gold medals at the 2004 and 2008 Olympics. She was part of the team that helped Russia win the right to host the 2018 World Cup. After winning her latest world title this week, Isinbayeva said she plans to take a break from the sport to have a baby.
Isinbayeva is to serve as "mayor" of one of the Olympic villages in Sochi and is an ambassador for the Youth Olympics.
Sochi organizing committee spokeswoman Svetlana Bobrova said the body had no reason to comment on Isinbayeva's statements.
"We like her and she is the mayor of the Olympic village," Bobrova told the AP.
It was unclear how many other Swedes or athletes from different countries made similar protests since the world championships started last Saturday. Hjelmer was eliminated from the heats in the 200, but Green Tregaro qualified for the final of the women's high jump and will return to the track Saturday.
A rainbow flag is often used as a symbol of gay rights and gay pride, an issue that has gained attention from Western activists and entertainers since Russia's anti-gay law was passed in June.
American middle-distance runner Nick Symmonds, who won the silver medal in the 800 meters, voiced his support for gay rights in a blog entry for "Runner's World" before the competition began.
Once in Moscow, Symmonds didn't want to comment on the issue, saying, "You're not allowed to talk about it here. I'll get put in jail for it."
In his blog, though, Symmonds wrote: "If I am placed in a race with a Russian athlete, I will shake his hand, thank him for his country's generous hospitality." Then, after beating his opponent badly, he would "silently dedicate the win to my gay and lesbian friends back home. Upon my return, I will then continue to fight for their rights in my beloved democratic union."
The law does not explicitly ban participation in gay pride parades or promotion of lesbian, gay, bisexual and transgender equality online, but anyone wearing a rainbow flag on the street or writing about gay relationships on Facebook, for instance, could be accused of propagandizing.
The International Olympic Committee and FIFA have asked the Russian government for more clarification. It remains unclear if the new law will be enforced during the Sochi Olympics or World Cup.
AP Sports Writers Raf Casert and Pat Graham, and Associated Press writers Jim Heintz and Leonid Chizhov contributed to this report.
Copyright 2013 The Associated Press.