I will not use the terms “liberal” and “conservative” in this answer because I do not think that attitudes on free trade divide very well into liberal and conservative points of view. For example, both Presidents Bush, along with President Clinton and President Obama have been in favor of free trade. Therefore, it is not at all clear that only conservatives are pro-trade.
My own view is that it might be better if we had less free trade. There would certainly be bad effects if we reduced the amount of trade that we engage in. On the other hand, we would probably have more economic stability.
I have no doubt that free trade is a good thing in many ways. For example, my own small town has just attracted a Japanese company that is building a plant here to make use of our cheap electric power. Were it not for free trade, it would be harder for them to do this. Perhaps more importantly, we all benefit from free trade when we buy cheap goods. If clothing were made here in the US, we would all have to pay more for it and we would be able to afford less clothing. If things like iPhones were made in the US, we could afford fewer of them. Therefore, free trade is really an attractive thing in many ways.
However, it does come at a price. Mainly, free trade hurts certain parts of our society. It helps to create situations in which people with less education and fewer skills cannot get good jobs like they good a few decades ago. This is really bad for our economy and, more importantly, for our society. When people without college degrees are essentially shut out of the middle class while, at the same time, they watch educated people get richer and richer, it is a recipe for anger. This is part of what drives such things as the Tea Party movement.
If we had less free trade, we would give up some of our standard of living. In return, though, we might get a society in which there is more opportunity for people with various levels of education. I think this would be a good trade. Surely we can do without some of our material goods if it will allow us to create more jobs for our fellow Americans.