These two phrases have similar, but nonetheless distinct, meanings.
So that if - this phrase is used when you are telling someone the purpose, reason or intent for which something has been done. In your sentence the use of so that if would imply that the space in front and behind her had been deliberately left free for the purpose of allowing her to turn ninety degrees in any direction to avoid making physical contact.
So if - this phrase is used to tell you the effect of something that has been done. In your sentence the use of so if would imply that the the result of having space in front and behind her was that it allowed her to turn ninety degrees in any direction without making physical contact. In this case there is no implication that this result was pre-planned, the result may have just been fortuitous.
If is not essential to these phrases, although it is essential in your sentence. For example:
I went to Melbourne so that I could go to the concert.
In other words, going to the concert was the reason or purpose for me travelling to Melbourne.
I am in Melbourne, so I can go to the concert.
In other words one of the effects of me being in Melbourne is that I can go to the concert, but that was not necessarily the reason for me travelling to Melbourne.