First of all, welcome to the forums.
In Conway's Game of Life (and other isotropic rules), symmetric starting configurations always stay symmetric, so a symmetric starting configuration that turns into a constellation that is symmetric, which seems to be a major reason for its aestheticness, wouldn't be perceived as interesting by most people here. I recommend that you read
the forum rules in order to get a better idea of what is and isn't considered notable.
That being said, while the ash of symmetric starting configurations isn't inherently interesting, many large natural still lives are symmetric because they only have to worry about one half stabilizing, so they tend to form from symmetric regions. Here are some examples:
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x = 19, y = 27, rule = B3/S23
9bo$8bobo$8bobo$9bo7$8b3o$7bo3bo$7b5o$3o13b3o$7b5o$7bo3bo$8b3o7$9bo$8b
obo$8bobo$9bo!
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x = 17, y = 19, rule = B3/S23
5bo5bo$5bo5bo$4bobo3bobo$2o13b2o$4o9b4o$b3o9b3o3$4b2o5b2o$4b3o3b3o$6b
5o$3bo3bobo3bo$4b2obobob2o$7bobo$6b2ob2o$6b2ob2o$6b2ob2o$6b2ob2o$8bo!
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x = 31, y = 16, rule = B3/S23
2bo25bo$obo25bobo$b2o25b2o6$14b3o$6bo17bo$5bob2o13b2obo$8bo13bo$8bo13b
o$6b2o5bo3bo5b2o$13bo3bo$13bo3bo!
I am tentatively considering myself back.