A valid argument against free trade? Recently I read Bertrand Russell's Political Ideals (1917). Although he expresses strong left-wing ideals there, he supports free trade and criticizes protectionism.

It seems that not any left-wing theorist agrees with Russell on this. As an example, I quote from A Darwinian Left (1999) by Peter Singer:


  What capitalists failed to accomplish by a century of repressive measures against trade union leaders, the World Trade Organization... is doing for them. When barriers to imports are removed, nationally based trade unions are undermined. Now when workers in high-wage countries demand better conditions, the bosses can threaten to close the factory and import the goods from China, or some other country where wages are low and trade unionists will not cause trouble.


Now, I know that there may be different opinions on this and that's the nature of a complex subject like economics. However, I can't resist the desire to know what serious students and scholars of economics think of this argument by Singer.
I can get to more technical papers, but it's not a big secret what you have quoted. E.g. The Economist quotes MIT professor John Van Reenen:


  But just because the size of the pie expands [due to free trade], it doesn’t mean that everyone is better off. There are going to be some losers whose slice of the pie is so much smaller that they would have been better off with less trade. However, because the overall size of the pie has got bigger, the government can compensate the losers which can still make everyone better off. [...] But remember: thanks to free trade, you can afford that [better welfare programs], because the overall size of the pie is bigger.


And Harvard prof. Dani Rodrik writes:


  there is one Stolper–Samuelson-like result that is
  extremely general, and which can be stated as
  follows. Under competitive conditions, as long as
  the importable good(s) continue to be produced at
  home – that is, ruling out complete specialization –
  there is always at least one factor of production that
  is rendered worse off by the liberalization of trade.
  In other words, trade generically produces losers.
  The proof of this result is simple enough to be
  stated quickly here. [the proof is still like half a page]
  
  More recent work in trade theory has emphasized
  heterogeneity among firms and workers. These
  models have additional margins for redistribution,
  between firms and workers that otherwise look
  quite similar. Grossman, Helpman, &amp; Kircher (2017), for example, enrich the Stolper–Samuelson
  framework by considering heterogeneity within
  broad worker categories. ‘‘Managers’’ and ‘‘workers’’
  must combine in teams, and their productivity
  depends on the quality of the match. Trade liberalization induces re-matching and generates distributional effects within occupations and industries,
  in addition to the standard effects across broad
  factors of production and industries.
  Hence in all these models, redistribution is the
  flip side of the gains from trade. No pain, no gain.


My point is not to say that these theoretical models 100% apply to the complex realities of international trade, but rather that economists are aware that under certain conditions some segment of the workforce can be worse-off with free trade... unless something else happens.

Nevertheless, the prevailing opinion among economists, or at least US academic economists surveyed by IGM is that the long term benefits of free trade outweigh the short-term negatives (including [un]employment in some sectors).



As the survey additionally collected fill-in comments/responses, they are an interesting reading, but the first one (alphabetically, from Acemoglu) probably summarizes the critique you inquire about:


  Economists often understate short-term employment costs, which are significant and unequally distributed, but probably less than benefits.


As an example of empirical work evaluating such effects in a concrete context, Caliendo et al. (2015)


  We
  find that China's import competition growth resulted in 0.6 percentage point reduction in the share
  of manufacturing employment, approximately 1 million jobs lost, or about 60% of the change in the
  manufacturing employment share not explained by a secular trend. Overall, China's shock increases
  U.S. welfare by 6.7% in the long-run and by 0.2% in the short-run with very heterogeneous effects
  across labor markets.


Related enough, a more recent IGM survey of a panel of European economists (some of which do work in the US though) shows that they are not blind to the effects of inequality on [liberal] democracy. The latter survey also poses questions on whether higher government spending is justified from this perspective. So compensating or at least caring for losers (not necessarily stemming from free trade alone) is also a topic that economists are not opposed to. (Whether they should talk more about it, is a different issue.)