I'm trying to get all these lined up.
Which of these are the major anti-gun bills you mentioned? And which of the two pro-gun Obama laws are you referring to?
1934 NFA was signed by FDR (D)
1968 GCA was signed by LBJ (D)
1986 FOPA (which expanded firearms rights considerably but also closed the machinegun registry) was signed by Reagan (R)
1989 "Assault Weapon" import ban was enacted (not a law, an Executive action) by Bush Sr. (R)
1993 The Brady Act imposing waiting periods and later background checking was signed by Clinton (D)
1994 AWB was signed by Clinton (D)
2005 The Safety Lock bill was signed by Bush Jr. (R)
2007 NICS Improvement Act (incentivizing states to report on mental health issues for the NICS system) was enacted by Bush Jr. (R)
2009 a bill allowing firearms in checked AMTRAK luggage was signed by Obama (D)
2012 a bill National Park carry was signed by Obama (D)
2016 or 2017 SSA notification of mental health issues to the FBI background check was enacted (not a law, an executive action) by Obama (D)
2017 SSA notification to FBI background checks rescinded by Trump (R)
2022 the BSCA expanding the 1968 GCA by increasing some background checks and trying to restrict private party sales was signed by Biden (D)
A lot of what Republicans have done have been on the state level.
Ronald Reagan signed the Mulford Act into law in California and instituted a 15-day waiting period.
George Deukmejian signed the Roberti–Roos Assault Weapons Control Act into law.
George Pataki signed NY's Assault Weapons Ban Act into law.
Rudy Giuliani led cities to sue gun companies out of existence and championed the Clinton AWB.
Mitt Romney signed MA's Assault Weapons Ban Act into law.
Larry Hogan banned bumpstocks, privately made firearms, and signed RFLs into law in MD. Along with supporting the MD AWB.
Rick Scott banned signed the FL's Parkland Gun Control bill which banned bumpstocks (and other similar accessories like FRTs), adults under 21 from buying a firearm, instituted RFLs and statewide mandatory waiting periods.
Phil Scott singed VT's magazine ban, UBC, mandatory storage, RFLs, and waiting period into law.
Dean Skelos as the NY Senate Majority Leader rushed the SAFE Act through and politically forced the Republican controlled Senate to pass the bill through at midnight for Gov. Cuomo.
Arnold Schwarzenegger signed CA's .50 caliber ban and microstamping bill into law.
As for Republican Presidents.
Reagan didn't stop BATFE's open bolt ban in '82.
George HW Bush via executive order banned the import of "assault weapons."
Both Bush and Reagan supported the Clinton AWB and Waiting Period.
George W Bush via executive order banned the import of "machine gun barrels." Bush also stated if the Clinton AWB reached his desk, he would renew it.
Trump via executive order banned the ownership of bumpstocks (which, his actions were just declared unconstitutional). Also championed for state to pass RFLs and Under-21 purchase bans. He congratulated FL Republicans for doing just that.
Gun owners typically win federally when Congress is under Republican control and the White House is under Democrat control.
Obama is a prime example of that. National Park carry is a huge win. It happened because Republicans added it as an amendment to must pass legislation for the Obama administration.
But when Republicans actually have both chambers and the White House, nothing gets done. A prime example of that was National Reciprocity. Majority Leader Mitch McConnell refused to bring the bill up for a vote in the Senate after it passed the House. The Republicans controlled both chambers, but McConnell let the bill die.
Federally, the best course of action isn't legislatively now. It is judicially since gridlock is the best thing we can hope for in terms of unraveling the behemoth that is the administrative federal state.
The biggest danger gun owners face is the state level though, and in a number of states, the avalanche of gun control started under Republican leadership.