Terror management theory: Is this a valid conclusion based on the conducted experiment?
Interestingly, the authors appear to have been aware of your concern:


  Given that the only difference between these groups involved a subject
  variable for which there could be preexisting differences in DTA, we
  included a third group of creationists who read a nonthreatening
  essay.


Since the evolutionist/anti-creation and creationist/control groups had very similar scores, there was seemingly no reason to suspect different baselines.  However, I agree with you that adding this third group may not have been sufficient to eliminate the potential for preexisting differences in DTA.

Dispositional DTA:

The study of preexisting differences in DTA baselines is relatively recent, and is called dispositional DTA.  This line of research is indeed showing significant variation in DTA between different groups in control conditions, variation in reaction to primes, and even variation in reaction to delay - see Mikulincer &amp; Florian (2000) for examples of all 3.  So in light of this, I would not take it for granted that evolutionists and creationists should necessarily have the same dispositions.

Curiously, a study by Friedman and Rholes (2009) found religious fundamentalism to be negatively correlated with dispositional DTA (ie, greater fundamentalism = reduced effects on DTA).  Although fundamentalism is not the same measure as creationism, it does suggest that evolutionists may even have higher dispositional DTAs.

Ultimately however, a (not independent) partial replication of Study 5 is reported in Hayes (2011) Study 4, in which pro-evolution participants are subjected to an anti-evolution prime or the same control material used in Study 5, and the same DTA measure is used immediately thereafter.  While not having the creationist contrast, this experiment measures the evolutionists/control baseline missing from Study 5, as well as the effect of anti-evolution material on evolutionists.  I do note that the criteria for selecting participants was slightly different than Study 5, but not substantially different (n=93).


  DTA was higher in the Threat condition (M = 2.26, SD = 0.98) than in
  the Control condition (M = 1.68, SD = 0.96).


The results seem to indicate that the authors' assumptions about evolutionists' preexisting DTA may be valid.

Implicit primes:

The alternative explanation that reading about evolution might raise DTA in all participants due to the nature of the topic does not fit well within the context of existing DTA research.  Explicit primes increase DTA only after a delay or distraction.  For the immediate effects on DTA found in Study 5, an implicit prime must be used - ie, one that does not directly elicit thoughts of death.  This is presumably what Studies 1-4 establish.  Also see Steinman &amp; Updegraff (2015) for a comprehensive review on the effects of explicit vs implicit primes on the need for delay.

In that context, had Study 5 not included evolutionists at all, the data gathered would have still been sufficient to conclude that reading about evolution increases DTA in creationists, substantiating the statement cited in your question.  The study's novel inclusion of a group with an opposing worldview adds some valuable information from which to consider additional conclusions.  That said, it would not be prudent in any case to make strong conclusions from a single, small, poorly controlled, unreplicated experiment.  In my view, this study has many flaws that I won't rant about here.  All I will say is:


Good on you for checking references, that is rare and commendable.
Good on you for applying critical thinking and questioning conclusions.


Re further references, the DTA hypothesis Wikipedia article contains many references to literature both supporting the cited statement and questioning the evidence for it.  Lots more on Google of course.