The opening session reflected a more raucous atmosphere under the dome of Berlin's Reichstag building, even though a new government won't be in place for weeks or even months. Other parties rejected Alternative for Germany's nominee as deputy speaker.
Schaeuble, a member of Chancellor Angela Merkel's conservative bloc, told lawmakers that a respectful style would be important in the new parliament.
Germany's new lower house has 709 lawmakers, a record size. It has six caucuses, up from four in the previous parliament. It includes 92 lawmakers from Alternative for Germany, or AfD, the first party to the right of Merkel's conservatives to enter parliament in 60 years.
AfD won 12.6 per cent of the vote last month after a campaign that centered on loud criticism of Merkel and her 2015 decision to allow large numbers of migrants into Germany. It also harnessed wider voter discontent with established politicians.
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"The people have decided and now a new era is beginning." Baumann complained that parliament's rules were changed earlier this year to have the longest-serving lawmaker, rather than the oldest, open the first parliament session, a change that deprived an AfD lawmaker the chance to give the opening speech.
Schaeuble, who has been in parliament for 45 years and had been finance minister since 2009, was elected as the new speaker by 510-173, with 30 abstentions. He ran unopposed, although AfD objected to him since he had previously described them as a "disgrace for Germany."
Lawmakers from mainstream parties object to comments in which Glaser indicated that freedom of religion shouldn't apply to Islam, which they say put him at odds with Germany's constitution.
It was not immediately clear whether the AfD would make another attempt to have Glaser approved, or move on to another candidate when parliament reconvenes in November.
Merkel's conservatives, the pro-business Free Democrats and the traditionally left-leaning Greens are in the early stages of trying to form a governing coalition.