I was on EI. I recently started a new job as an employee. There were 2 phone calls and then I started working the next day. There's a few things that make me concerned for my health (even as simple as the uniform is just a t-shirt and we can't wear jackets on top etc)
If I quit in probation can I go back on EI?
Here is a page describing when you can collect EI after quitting your job voluntarily.
The simple summary is that you will be paid EI if "The only reasonable alternative for you is to quit your job".
Health issues are a valid reason but it's not as simple as "I think the work is unhealthy". Your concerns need to be reasonable and justified, and you also need to have gone through a process with your employer to try to get the problem fixed.
For example, you give a concern as "made to wear a t-shirt without being able to put a jacket over it". If you are outside in the snow doing construction that's obviously a major safety concern. If you are indoors in an environment where a t-shirt is reasonable then it wouldn't be.
You have to have worked with your employer to get the concerns addressed, and you will have to show that your concerns were reasonable and justified.
Here is a page about the right to refuse unsafe working conditions. You should also report unsafe working conditions, but that is a provincial responsibility and you will have to find the place for your province.
To expand a bit more, based on your comments: generally if you are let go from your job you can claim EI. But if you were fired for a good reason (like not showing up or refusing to do your job) then you won't get it.