I'm starting to see another advantage of getting older: You've actually lived through historic events and know what really happened as opposed to spin done nearly 20 years later.
First, I'll concede that this was political game playing on the part of the Democratic Party. However, unlike the complaint against Obama, the Dems were not objecting to Bush being in schools as some kind of infringement on parental rights. Please see this paragraph from the article you posted:
With the Post article in hand, Democrats pounced. "The Department of Education should not be producing paid political advertising for the president, it should be helping us to produce smarter students," said Richard Gephardt, then the House Majority Leader. "And the president should be doing more about education than saying, 'Lights, camera, action.'" (emphasis added by me so readers will see the motivation of the complaint)
It was an election season leading up to the primaries when Dems hoped to get more attention on their challengers to incumbent G.H.W. Bush. GHW's ratings were dropping in the polls due to economic issues, but he was the best the Republicans could offer and so he was running for a second term.
The objection was that Bush was using the Office of the President and Department of Education resources to make him look good to voters and to pitch his education plan to voters so he would be re-elected.
The objection was not a challenge to any president ever speaking at a public school nor a declaration that presidents should never be allowed to talk to children nor that Bush was corrupting the minds of children nor indoctrinating them to his beliefs, but that Bush was using his appearance as a photo opportunity to sway the minds of adult voters.
This is a common argument waged against incumbents during election season, not just presidents but also governors, regardless of political affiliation. Presidents have the advantage of looking presidential, a benefit the challenger cannot have simply because he/she is not the president.
I realize some readers may not trust this information. The best way to check it is to get access to the Washington Post archives and read the old clips within the context of the election year.
Furthermore, Bush's speech was televised and since it's clearly stated in the clip provided in your comment above that the GAO ruled there was nothing improper about George H. Bush's action even though it was given in election season, less credibility may be given to Obama's opponents who believe his speech today was improper.
On another point, please consider that while conservatives are very upset that Obama White House spokesperson Gibbs called conservative objections more of "silly season," the New York Times of 1991 reports Republicans had similar language for Dems back then:
The President's spokesman, Marlin Fitzwater, responded by denying that Mr. Bush's talk to the schoolchildren had been a political event and calling the criticism "nonsense."
News delivered without the context of history or the state of the nation at the time, such as it being on the cusp of an election year, can be misleading. And of course, election season is the season for silly objections and investigations, but we're not in election season at the moment.