I'll let someone who lives in Taiwan comment further, but I was just in Taipei for a brief trip with my husband and found that it was not an issue. Homosexuality is not illegal, gay bars and venues are publicly acknowledged, in districts like Ximending you can see couples holding hands, and so forth. I would consider it a bit more accepting than Tokyo, and around the middle of the spectrum of what you would find across the entirety of the United States.

In general I've found most of Asia to be perhaps not accepting, but polite. Taipei is not like San Francisco or Berlin, but isn't unsafe and it won't be a problem getting a date (supposing that you like asian men, of course).