Yes, organisations try to be diverse and inclusive. There are challenges in achieving the actuals.
Unfortunately, people confuse diversity only with the number of women in the organisation. There are more facets to it when the organisation tries to be inclusive.
Take this example, an mnc in Hyderabad would normally have a large % of Telugu speaking population, so does Tamil in Chennai. The organisation can be inclusive in sensitising the native employees not to communicate in the official meetings in the local language but when it comes to implementation, it largely depends on the team.
Tl;dr Organisation can provide an environment and policy framework but diversity and inclusion happens when employees are open to it.
Pay disparity is treated more seriously in US than in India however, an organisation would never discriminate against a woman. The benchmarks we get from industry are gender agnostic so are the compensation frameworks.
Pay disparity largely arises due to different points of salary at hire.
Again, during appraisals these are subject to manager biases though we always compare the possibility of disparity before rolling out increments.
At grassroot levels, your visibility will be limited to the team you're working on. Some men in your team might feel a woman is compensated more and will blame the manager to favouring women. Some women in your team might feel they are at a disadvantage just because she's a woman.
I'm not denying the disparity that exists in pockets but an organization level, we do not discriminate between gender and always try to maintain parity with the same bands as well as new and existing hires.
P.S. Current generation of workforce (gen z) doesn't stick for very long in the companies to see these changes happening. Ask anyone who spent a fair deal of time in the corporate, say 10-15 years and you'd realise how much have we moved forward.