Dichotomizing continuous variables for an EXPERIMENT not a survey I've aware of the many issues/pitfalls with splitting continuous variables in survey research. Nothing I have read addresses whether doing so to create groups which will then be assigned to tx conditions in a field experiment is ok, or less bad. (or worse?) 
For example:  Social Dominance and Justice System reform. I want to assess the effectiveness of two anti racism workshop styles for persuading people. One uses a colorblind (CB) type message (e.g. we are all the same), the other uses a valuing diversity (VD) (e.g.: we are different and that is good) style message. I have reason to think these messages will have different impacts depending on participants' social dominance orientation. 
So I want to split SDO scores into HI-LOW (1 SD above and below the mean on a prescreen) and assign half of each group to each treatment condition CB or VD, for a 2x2 design. I'm predicting support for justice system reform measures.  
I'd love to get some input on this question. Citations would be especially helpful.
Clarification: Ss were drawn from a large prescreening session and I needed SDO homogenous groups for the workshops. There is reason to think that SDO homogenous (ish) groups may matter for the workshops to work as intended.
 A: It still seems like you're throwing a lot of data away and not getting anything in return.
In addition to losing information about each subject's individual SDO score, you're going to end up rejecting a lot of subjects  if you only enroll subjects that are at least 1 SD from the mean: around 68 percent, if SDO is normally distributed, potentially more if the scores have heavy tails. 
Your analysis strategy would not change. There are still two factors: workshop type, coded as an indicator variable, and initial SDO score. Your hypothesis remains the same: "there is an interaction between the factors", but you may end up with a bit more power to detect an effect. 
The results are also easier to visualize: draw a scatter plot of Support vs. SDO Score and color each point according to the workshop type. 
I might grudgingly consider binning the SDO scores if I wanted the results to be accessible to others who use the same thresholds--perhaps there's a short form of the SDO questionnaire that only spits out LOW, TYPICAL, or HIGH. Even if this were so, I'd suggest just indicating them on the graph instead. 
