Should we use an infinitive or gerund / present participle after the adjective 'crucial'? 

Should it be 'it is crucial to quitting smoking' or 'it is crucial to quit smoking'?

If you think both look correct, you are right. However, the word 'it' means different things in these two examples.

'It is crucial to quitting smoking.'

'It' is a pronoun here, and refers to something that helps you to quit smoke, such as 'stopping seeing friends who smoke', 'seeing a doctor' or 'motivation'.

'It is crucial to quit smoking.'

In this sentence, the word 'it' is a 'dummy pronoun' which has no particular meaning. It is the subject placeholder for the infinitive clause placed at the end of the sentence, i.e. 'to quit smoking'.

In fact, you can rewrite this sentence to this:
e.g. To quit smoking is crucial.

In this example, it is clear to us that 'to quit smoking' is the subject of the sentence.

Both 'To quit smoking is crucial.' and 'It is crucial to quit smoking.' means 'you must stop smoking'.