Should Poetry should have the same meaning to all people?

There are several different techniques for analysing a poem: practical criticism, close reading, lexical analysis, gender studies oriented, marxist and formalist are only some of the different schools.

But how you analyse a poem will depend on what you want to do with it (what the purpose of your analysis is) - or else on the method your teacher prefers.

Any good analytical technique can be applied usefully to all poems alike.

So the analysis technique you apply to a poem, doesn't depend on the poem. (It depends on the critic).