The first approach is accurate, the second approach is wrong:
1a. Science helps us understand nature, vs.
1b. People who do science help us understand nature.
Science, in general (I am a scientist) does help us understand nature. But not all people that do science help us understand nature, some people that do science are frauds, some are seeking wealth and do not intend to share their knowledge. 1a is more accurate.
Can science perform an action like helping? Yes, of course. A step ladder can help me reach a high book shelf. Science IS understandings of how things work, from protozoans to galaxies, of course those understandings help us understand nature.
2a. Western culture pursues worldwide equality.
2b. The people of Western culture pursue worldwide equality.
Again, not all people of Western culture do this, a large percentage are only out for themselves, some would literally return to the days of legalized slavery. (2b) is an over generalization that just isn't true.
Can Western culture perform an action like pursuing? Presumably, a culture can be pursuing something; it is composed of people that can come to some consensus. More than other cultures, the people of Western cultures have a consensus that equality is a good thing; but I wouldn't go so far as to say they actively pursue it, most seem to just hope it happens. But that is a quibble; cultures can take actions and pursuit is one of them. Wall Street culture pursues profit.
3a. That company seeks to promote a product.
3b. The people of that company seek to promote a product.
Again, 3b is not accurate, most people in that company have other jobs, only a few in the marketing department actively seek to promote their products. Others are focused on accounting, payroll, hiring, engineering, programming, janitorial work, purchasing, receiving, manufacturing, shipping, etc.
Can that company perform actions such as seeking and promoting? Sure, the company is an entity in itself, composed of people, and in this case an explicitly thinking entity, organized to pursue objectives.
The key to all these examples is understanding how people use and understand words. "Help" does not have to be a physical action; the amorphous "Science" helps us understand nature because we read and understand the work and explanations of other people. Those scientists helped us, but not actively in person, their recorded understandings helped us, and we call those recorded understandings "science."
A culture is much the same; a collection of principles, beliefs and rules subscribed to by a body of people. Those could translate into a belief that positive action should be taken and rules made to eliminate inequalities whenever they are discovered or creep into their society, a culture like that could be characterized as pursuing equality. I just wouldn't say Western culture holds those beliefs.