Women's bodies should not be used in sports or games as billboards for the political or religious agendas of others. Or course, nor should men's bodies be billboards. But in sports and games this problem manifests itself much more often for women than for men.
Religious women who cover for religious reasons, such as some Muslim and Orthodox Jewish women, should be free to come as they are to compete, so long as fairness and safety can be accommodated. Those who want to promote extreme secularism and ban religious garb in sports are wrong to try to use women's or men's bodies as a platform to promote their ideological, political agenda. Read about the Hijab Hurdle in Sports.
The other side of the coin is that in order to compete women should not face a requirement to wear religious garb or political symbols with which they disagree.
If the Islamic Republic Iran does not stop requiring non-Muslim competitors to wear an "Islamic head cover," as it is called in Iranian law (i.e. the issue is religious, not one of cultural modesty), international sports and game federations should stop allowing Iran to host women's tournaments.
So too the U.S. Soccer Federation and the Football Association of Ireland need to stop violating FIFA rules, including risking violating players' consciences, by requiring players on the national teams to wear an LGBT rainbow political symbol in order to be allowed to play. This problem has caused particular harm to a female soccer player. Those who want to promote a particular political agenda in sports are wrong to try to use women's, or men's, bodies as a platform to promote their politics.
Read about the need to End Iranian and American Garment Coercion in Sports and Games.
International sports need to respect international human rights. This includes Article 18 of the International Covenant on Civil and Political Rights (ICCPR).
ICCPR Article 18.1 "Everyone shall have the right to freedom of thought, conscience and religion. This right shall include freedom... to manifest his religion or belief in worship, observance, practice and teaching."
ICCPR Article 18.2. "No one shall be subject to coercion which would impair his freedom to have or to adopt a religion or belief of his choice."
Sports and games need to include freedom to wear religious garb, so long as fairness and safety observed, if a competitor so choses. And sports and games need freedom from coercion to manifest a religion or belief with which competitors disagree.