Racism, sexism, homophobia, transphobia, ableism ARE all structural problems because (while they may have pre-existing oppressions before capitalism) capitalism utilises these oppressions. Sexism/homophobia/transphobia result from the gendered division of labour. Racism is the result of colonialism, slavery, and capitalist expansion (and has been utilised by capitalists to divide the working class and create a stratified labour market (ie workers with full rights, migrant workers with rights but some restrictions, migrant working illegally or the stratifications resultant from slavery in the USA). Ableism results at least partly from class society, the labour market, and the value placed on work (ie if you are working class but you can't work as fast as is needed or you need adjustments, or some you are unable to do some types of work or need care) and the individualisation of society. Where some of these oppressions have reduced in their impact or changed in how they are structured in the last years/decades its is partly because of our organisation (whether anti-oppression or class based) but also because capitalists has found a way to incorporate some of these demands in neoliberalism.
None of us (including the unions, the left, radicals, feminists, anti-racists, LGBT activists) are outside the structure of this society. We are all inculcated with racist/sexist/homophobic/transphobic/ableist attitudes because we are socialised into this society - and it takes a process to overcome this. Therefore it is not surprising that despite believing that "an injury to one is an injury to all" some trade unionists and left and radical people have acted or organised in racist, sexist, homophobic, transphobic, or ableist ways and many have not fully supported the fight against these oppressions. It also means that many working class people who are oppressed in these ways may experience much of this oppression - violence, abuse, bullying, ostracism, harassment - from other working class people - and for this reason autonomous organising with people who experience the same oppression is sometimes necessary. Undoing internalised oppression and forming an identity/the ability to name an oppression is also sometimes a necessary process which also needs autonomy.
This autonomous organising very often is working class people [LGBT people, for example] organising together, and its a bit disingenuous to suggest otherwise. The problem is that there are also parts of the feminist movement, the LGBT movement, etc organised by people who are part of, or wanting to become part of, the capitalist class - and some of the reforms they want might seem to have the potential to change things for the better for women, LGBT people, etc in general - though of course they will never get to the root of the problem. So without a structural analysis that includes class the organising efforts of oppressed working class people can be co-opted into these cross-class movements and incorporated into neoliberalist reforms. This is what I think of as identity politics.
This isn't inevitable however - there's a long history of organising efforts by working class women, LGBT people, black people, disabled people, etc that does follow a structural analysis - aimed at challenging state violence and oppression or violence and oppression from other parts of the working class, aimed at changing unions and other working class organisations to respond to oppression or forming new working class organisations that do that, and expanding autonomous action to give and receive solidarity. This to me is not identity politics in the main (though as none of us are outside of the structures of society of course sometimes organising and analysis is influenced by identity politics, neoliberalism, and oppressive attitudes).
