I sent a mail visa application to the Royal Thai Embassy Consular office at 2300 Kalorama Rd on March 27, 2018.
My USPS tracking shows that the mail application had been received.
No update since then, when I call or email Thai embassy consular there is no reply. 

How long did people have to wait before they got their tourist visa accepted?

My travel dates start on April 14, do I have enough time? 
 
 

It appears that you submitted an application for a tourist visa by mail to the Royal Thai Embassy consular section in Washington DC. According to https://thaiembdc.org/consular-services/tourist-visas/category-tr/ the processing time for a mail-in application is 15 working days. A quick estimate suggests that 15 working days will be up on April 10 (I have not carefully checked the embassy holidays between March 27 and April 10, only counting April 8.). There is not much slack in this schedule, but it appears you are more likely than not to be lucky.

Their website states 15 days for mailed in applications. But normally it is about 10 days from what others have reported.

I think you should have it back next week. I suggest you try contacting them on Tuesday (closed for a holiday on Monday) about your visa. I assume you calling the numbers at the bottom of this page. https://thaiembdc.org/consular-services/tourist-visas/category-tr/