What left wing ideas would identity politics be in competition with/ opposition to?
This is a really good question, and I hope you get a lot of replies to it which will probably illustrate my in a nutshell "a lot, but from different perspectives".
My own take on it is this:
Left politics are socialist. The underlying principle is working towards a fairer society. When you look at this closely, you see that a fairer society means that the people who have too much should give it to the people who have too little. That's in economic terms, but it also applies to fairness in how people live their lives i.e. not to be oppressed by the people who have the power. This means that power should be redistributed as well.
When you look at who is advantaged by wealth and power, it's defined by our class system. It's concentrated in the ruling class (aristocracy, upper class, corporate heads of business, magnates etc) and filters down through the professional/middle class until it gets to the working class and then the impoverished. There's a whole mass of ways that wealth and power are distributed and exercised within all that, but that's the general idea.
Where do the ruling and middle classes get their wealth and power from? Some of it's inherited and passed down through the generations "old money". Most of it is gained from elsewhere in society. Our entire capitalist system is set up to extract as much wealth as possible from the people that produce things of worth that make a profit, and for that profit to be redirected to the already wealthy and powerful. So there's loads of us working very hard to keep a roof over our heads, and provide for our families in the full knowledge that all that effort earns the least wages they can get away with but that produces a huge amount of profit for the people in charge. This affects everyone whether able/willing to work or not. So not very fair. People on the left want to change that and so are anti-capitalist. I tend to think of anti-capitalism as a force being exerted upwards against the capital force being exerted downwards.
But power is distributed in another way too, because the capitalist system is also patriarchal. Our society is structured in such a way that it favours male dominance. So people on the left challenge that as well, because the converse of dominance is oppression which does not make for a fair society. Other ways that patriarchal power is used to dominate/oppress is by way of dominating anything "other" e.g. race, colour, culture, disability, orientation, gender, age etc (in no particular order). People on the left want to change that and so are anti-patriarchy. I tend to think of anti-patriarchy as a force being exerted around and up against the patriarchal force being exerted around and down.
Where it gets tricky is where anti-patriarchy is concentrated on to the exclusion of anti-capitalism, and this is known as identity politics. Not all identity politics are left, simply because that really wouldn't suit some of the rich and powerful identities whose economic and power interests it wouldn't serve. Identity politics don't make for a fairer society because they only aim for anti-patriarchal fairness which only looks at part of the picture. They are also divisive and result in segregation, with sharp lines being drawn between "us" and "them".
A bit simplistic, just a bit of an overview. There's loads of different flavours of "left" too.