No, globalisation didn't speed up under Clinton.Yeah cuz globalization didnt speed up under Clinton (NAFTA). It isnt a republican or democrat issue, they both did this.
NAFTA was more of an amendment to the US-Canadian trade bloc that already existed, and essentially eliminated tariffs between the US and Mexico, and George HW Bush is the one that negotiated NAFTA. The drops in manufacturing jobs were going to happen regardless, because of technological advancement, the trade also created hundreds of thousands of jobs, even if it helped eliminate hundreds of thousands. Neoliberal idealism is definitely a far more "conservative" idea than it is a "liberal" idea, even if (here in the US especially) both are neoliberal.
http://www.nber.org/papers/w21906.pdf
Definitely check this out if you get the opportunity, China's hyperurbanization and industrialisation had far more of an impact on the US jobs than NAFTA.