Is it safe get Botox Cosmetic or Dysport if I'm heterozygous for the MTHFR mutation (C677T)?

Most likely since the injection remains localized there should be no problem.  The possible lack of this enzyme has a bearing on your vitamin metabolism but should not affect the toxin effectiveness or have any side effects

Yes, you are fine to receive Botox injections with the MTHFR mutation.  This mutation is fairly common in the heterozygous form and can be found in up to 50% of the population.  Most people who are carriers do not display any abnormal traits from the variant gene.  Homozygous variants, and some heterozygotes, may see a decrease in the metabolic pathway that converts folate and folic acid (vitamin Bs) into active forms.  There can be a build up of homocysteine (amino acid) which has been linked to cardiovascular issues.  However, the MTHFR mutation (especially heterozygous) should not interact with the metabolism and elimination of Botox.