If 0 work has been done and the task was schedule in the past then you can't avoid the Project-imposed constraint.
If >0 work has been done and you have (Tools | Options | Schedule-tab) "split in-progress tasks" checked then the task can be split with the remaining portion of the task starting on the Status date. You will have a two-step process here:
1. Enter all work done on your tasks.
2. Select the tasks you want to be updated (those where work has been done and those that should have started and have not and have 0 work done) and then (on the Tracking toolbar) click on "Reschedule Work" button.
If 0 work has been done the start date will be adjusted to the Status Date and a constraint will be imposed.
If >0 work has been done then this will split the task moving remaining work to start on the Status date.
By the way, what you are trying to do is not a particularly good use of your time. Once the schedule is under way, you shouldn't worry about these Project-imposed constraints - just let it happen. You (as it appears you are doing) *should* be worrying when you impose them as you construct the schedule. But, even then, real world scheduling -- as opposed to theoretical world scheduling -- really does mean you'll will find that there times when you really do have to use SNET constraints.
If I were you, I'd be more concerned about actual vs. baseline. From what you've written, it seems to me that you very likely did create a baseline and have been baselining new tasks as they were added (using appropriate change control mechanisms when necessary). With all the good work you're doing, you should start focusing on Earned Value. In P2003 press F1 and in the search box type "Earned Value" -- there's some good reading there.