Best Way to Handle user triggered task (like import data) in Django
You can dissect your problem into the following steps:

User specifies task parameters
System executes task
System displays result to the User

You can either do all of these:

Sequentially and synchronously in one swoop; or
Step by step asynchronously.

Synchronously
You can run your script when generating a response, but it will come with the following downsides:

The process in the server processing your request will block until the script is finished. This may or may not affect the processing of other requests by that same server (this will depend on the number of simultaneous requests being processed, workload of the script, etc.)
The client (e.g. your browser) and even the server might time out if the script takes too long. You can fix this to some extent by configuring your server appropriately.

The beauty of this approach however is it's simplicity. For you to do this, you can just pass the parameters through the request, server parses and does the script, then returns you the result.
No setting up of a message queue, task scheduler, or whatever needed.
Asynchronously
Ideally though, for long-running tasks, it is best to have this executed outside of the usual request-response loop for the following advantages:

The server responding to the requests can actually serve other requests.
Some scripts can take a while, some you don't even know if it's going to finish
Script is no longer dependent on the reliability of the network (imagine running an expensive task, then your internet connection skips or is just plain intermittent; you won't be able to do anything)

The downside of this is now you have to set more things up, which increases the project's complexity and points of failure.
Producer-Consumer
Whatever you choose, it's usually best to follow the producer-consumer pattern:

Producer creates tasks and puts them in a queue
Consumer takes a task from the queue and executes it

The producer is basically you, the user. You specify the task and the parameters involved in that task.
This queue could be any datastore: in-memory datastore like Redis; a messaging queue like RabbitMQ; or an relational database management system like PostgreSQL.
The consumer is your script executing these tasks. There are multiple ways of running the consumer/script: via Celery like you mentioned which runs multiple workers to execute the tasks passed through the queue; via a simple time-based job scheduler like crontab; or even you manually triggering the script
The question is actually not trivial, as the solution depends on what task you are actually trying to do. It is best to evaluate the constraints, parameters, and actual tasks to decide which approach you will choose.
But just to give you a more relevant guideline:
Just keep it simple, unless you have a compelling reason to do so (e.g. server is being  bogged down, or internet connection is not reliable in practice), there's really no reason to be fancy.
The more blocking the task is, or the longer the task takes or the more dependent it is to third party APIs via the network, the more it makes sense to push this to a background process add reliability and resiliency.
In your email import script, I'll most likely push that to the background:

Have a page where you can add a task to the database
In the task details page, display the task details, and the result below if it exists or "Processing..."  otherwise
Have a script that executes tasks (import emails from gmail given the task parameters) and save the results to the database
Schedule this script to run every few minutes via crontab

Yes the above has side effects, like crontab running the script in multiple times at the same time and such, but I won't go into detail without knowing more about the specifics of the task.
I need your opinion on a challenge that I'm facing. I'm building a website that uses Django as a backend, PostgreSQL as my DB, GraphQL as my API layer and React as my frontend framework. Website is hosted on Heroku. I wrote a python script that logs me in to my gmail account and parse few emails, based on pre-defined conditions, and store the parsed data into Google Sheet. Now, I want the script to be part of my website in which user will specify what exactly need to be parsed (i.e. filters) and then display the parsed data in a table to review accuracy of the parsing task.
The part that I need some help with is how to architect such workflow. Below are few ideas that I managed to come up with after some googling:

generate a graphQL mutation that stores a 'task' into a task model. Once a new task entry is stored, a Django Signal will trigger the script. Not sure yet if Signal can run custom python functions, but from what i read so far, it seems doable.
Use Celery to run this task asynchronously. But i'm not sure if asynchronous tasks is what i'm after here as I need this task to run immediately after the user trigger the feature from the frontend. But i'm might be wrong here. I'm also not sure if I need Redis to store the task details or I can do that on PostgreSQL.

What is the best practice in implementing this feature? The task can be anything, not necessarily parsing emails; it can also be importing data from excel. Any task that is user generated rather than scheduled or repeated task.
I'm sorry in advance if this question seems trivial to some of you. I'm not a professional developer and the above project is a way for me to sharpen my technical skills and learn new techniques. 
Looking forward to learn from your experiences.