Are added yogurt cultures harmful to the gut?
I'm not sure what you mean by 'synthetic' gut bacteria, so I can't address that. is yogurt harmful to the gut? I believe the answer is no.

Women (and their doctors) have long known that taking antibiotics can result in Candidia (a yeast infection). Physicians have been advising women taking antibiotics to eat yogurt with live cultures, including lactobacillus spp. and bifidus spp. In keeping with today's movement towards evidence based medicine, Natural Medicines Comprehensive Database rates effectiveness based on scientific evidence according to the following scale: Effective, Likely Effective, Possibly Effective, Possibly Ineffective, Likely Ineffective, Ineffective, and Insufficient Evidence to Rate.

The effectiveness ratings for (just) LACTOBACILLUS are as follows:

Likely effective for:


  Diarrhea in children caused by a certain virus (rotavirus). Children with rotaviral diarrhea who are being treated with lactobacillus seem to get over their diarrhea about a half day earlier than they would without this treatment. Larger doses of lactobacillus are more effective than smaller ones. At least 10 billion colony-forming units during the first 48 hours should be used.


Possibly effective for...


  
  Preventing diarrhea in children caused by antibiotics.   
  Preventing diarrhea in hospitalized adults. Drinking a specific beverage containing Lactobacillus casei, Lactobacillus bulgaricus, and Streptococcus thermophilus (Actimel, Danone) twice daily during antibiotic treatment and for a week afterwards significantly decreases the risk of developing diarrhea.
  -Preventing diarrhea due to traveling. Taking a specific strain of Lactobacillus rhamnosus, Lactobacillus GG (Culturelle) seems to help prevent diarrhea in travelers.   
  Preventing diarrhea due to cancer treatment (chemotherapy). There is some evidence that patients with cancer of the colon or rectum have less severe diarrhea, less stomach discomfort, shorter hospital care, and require fewer chemotherapy dose reductions due to GI side effects when they take a particular strain of Lactobacillus rhamnosus, Lactobacillus GG (Culturelle).
  Colic in babies. Taking a specific Lactobacillus reuteri product seems to be more effective than using the drug simethicone.
  Lung infections. Children ages 1 to 6 years who attend daycare centers seem to get fewer and less severe lung infections when given milk containing lactobacillus GG or a specific combination product containing both Lactobacillus acidophilus and Bifidobacterium (HOWARU Protect).
  Treating a bowel condition called ulcerative colitis. Some research suggests that taking a specific combination product containing lactobacillus, bifidobacteria, and streptococcus might improve symptoms. 
  Treating irritable bowel syndrome (IBS). There is some research showing that certain strains of lactobacillus, but not others, can improve symptoms of IBS such as bloating, and stomach pain.
  Treating vaginal infections caused by bacteria (bacterial vaginosis). 
  Treating and preventing eczema (atopic dermatitis) in infants and children who are allergic to cow’s milk. 
  Helping prescription medications treat Helicobacter pylori (H pylori) infection, which causes stomach ulcers.
  Treating diarrhea caused by the bacterium Clostridium difficile.
  


Though some of the recommendations are for specific probiotic formulations, one can achieve similar results by reading yogurt packages and mixing types to assure coverage with the proper bacterial spp.

National Institutes of Health