Is the following sentence grammatical?
To proceed setting up your account, click here.
I'm suspicious of the word proceed in this context — isn't the word continue a much better fit?
I agree. "Proceed" needs a preposition like "with", "against", or "to". "Continue" can be used with a preposition but does not require one.
In your case, there are probably some initial steps to be taken before setting up a web site such as "paying money" or "filling a form of personal information" e.t.c. So, setting up a web site is another new step after those steps.
If so, I would use proceed to.
Also, proceed to and proceed with may slightly differ in meaning / sense
In your case, using continue might also be possible. But you should be careful with the context. The closest senses of continue:
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