There isn't a fixed yes or no answer to this question - it depends on your circumstances and yourself.
Personally, I think it is extremely helpful for people going into the study of Islam to have another career or vocation. This keeps you from financial dependency or desperation and makes you more free to study what you like for however long you feel is beneficial. This is especially if you are female and financially responsible for yourself or others, since men have certain financial opportunities that women don't; for instance, most imams of mosques are men, and usually men have more opportunities for paid services such as tabligh and majalis.
Then, in the future, if the opportunity arises, you could shift to work in the area of Islamic studies, or full-time studies, if that is what seems right.
So, you could try to do both - that is, maintain a separate job or career path, and do Islamic studies part-time on the side. (If you are not already doing this, and if you have the time and energy for it, of course - it is a commitment.) This would also allow you to see if it is right for you; for instance, some people think they want to go to hawza or do full time Islamic studies, but then decide after a couple years that it's not the right thing for them, and then sometmes it is a lot of work to get back onto a different career track.
Of course, the drawback is that you will miss out on an immersive experience, such as living at a hawza, but it can be a good way to feel things out.
You could consider what career you might pursue after your studies - for instance, working at a mosque, chaplaincy, university teaching, madrasa teaching, writing/translation, counselling, tabligh, or something completely different - and how available work is in that area, and much you would expect to earn.
You could also consider your skill sets that you would use after your studies - for instance, whether you feel most comfortable with things like leadership, management, oratory, social work, academics, and so forth. Of course, sometimes we discover that through experience.
Conversely, you could also look at yourself as an engineer - is it something that suits you and feel like you would miss if you left it and see a future for yourself in, or is it something you don't think you would get much further with or feel blocked in.
If you are 100% committed to pursuing Islamic studies, don't worry about negativity from people around you; however, it is still good to pay attention to some of the practical considerations they might bring up.
Similarly, if you are 100% committed to pursuing Islamic studies, then I would say just trust in Allah and go forward with it. The above advice is for if you are not certain.
Sometimes, Allah makes the decision easy for us by forcing us one way or the other! However, in the meantime, of course, pray for guidance and talk to people around you.
Allah does sustains us, but the reality is that many people who work in this area suffer from financial frustrations, unless they have a secure and suitably paying position of some sort, or other resources (inheritance, investments, etc).
I will leave you with a short story. Back in my younger years, when I was attending university, I used to study computer science (which was very competitive to get into and we were considered the lucky ones who were on top of the world). I decided that I was going to pursue Islamic studies and begin that by changing my major to Near Eastern Studies (the closest thing to Islamic Studies).
So, I went to one of our professors, a well-known Muslim, and told him the good news. "I'm going to change to a Near Eastern Studies major," I said.
He looked at me and said just one word. "DON'T."
Anyway, I did it anyway, but I have come to understand why he said what he did.