A cheering throng of 15,000 people - many waving flags, shaking Bibles and toting children - roared a denunciation of the Equal Rights Amendment today as an all-out assault on the American family.

Having filled the Astro-arena to the point where police at one time would allow no more people to enter, the crowd staked its claim as the voice of the majority in the continuing national struggle over the issues of women's rights, abortion and homosexuality.

Their highly publicized rally coincided with the first business of the National Women's Conference across town as feminists there sought to prepare a legislative agenda for women.

The two gatherings have thus riveted nationwide attention on the nation's fifth-largest city as rival elements seek to stop or further a movement that began 10 years ago and has since begun to reshape the lives of American women and thus the lives of men.

But the speakers at this rally - and, by the cheering endorsements of them, the crowd too - made clear their preference for historic sex roles.

With heavy reference to homosexuality, federally sponsored child care and what the speakers claimed would be the effect of the ERA, Phyllis Schlafly told her followers: "We reject the antifamily goal of the Equal Rights Amendment and the International Women's Year. The American women do not want ERA, abortion, lesbian rights, and they do not want child care in the hands of government."

And to a great cheer, Schlafly, the head of two organizations challenging the women's movement and the organizer of this rally, said, "You can turn back this tide. If you stick with us, the ERA will die 16 months from Tuesday."

That is the deadline for ratification of the ERA, currently stalled three state votes short of becoming law.

Religion hung heavy over this assemblage, which also served as a political baptism, for many who said they had never before spoken out. "I just couldn't sit back any longer," said Kenneth Ramay, 32, of Houston, who was here with his wife, Betty, and 6-year-old son, Brian, and who cited biblical quotations. "And I doubt very seriously that it will be the last" rally.

The crowd was almost exclusively white, Predominantly female and extremely strong in numbers of younger women, for whom questions of family and children hold a timely appeal.

"I want to keep my child at home and I don't want to be drafted," said Gale Hartschuh, 21, of Houston as she stood by the stroller containing her 2-month-old daughter, Wendy. "I'm afraid of what ERA will do to homelife."

Anti-ERA groups have repeatedly asserted, and pro-ERA forces have disputed, that adoption of the amendment could lead to the blurring of gender identity. Strangely enough, a men's restroom at the arena had been temporarily relabeled and taken over by a long line of women and at least one man was directed into a locker room occupied by women.

Perhaps no one caught the crowd today the way state Rep. Clay Smothers of Dallas did. With the pacing of a preacher, the black delegate repeatedly brought his audience to their feet with such declarations as "I want the right to segregate my family from these misfits and perverts."

Smothers also received cheers when he said, "I resent the fact that I have to come all the way from Dallas - spend my money to come here to try to prevent the federal government from promoting perverts." And as the gathering drew to a close, large cardboard buckets were passed across the rows of the faithful. Currency fluttered in and one woman from Oklahoma was seen writing a check for $100, which was placed in a bucket next to a bright yellow check for $50.