Is there an idiomatic way to express 乱说 or 胡说八道 in an elegant way?
Basic

没有根据 unfounded
不合逻辑 illogical
不可信 untrustworthy
没有说服力 unpersuasive


Advanced

信口开河：说话没有根据，不可靠。（嘴巴随意张开。信口：随口。开河：原为开合。）
信口雌黄：不顾事实，随口乱说或妄作评论。（雌黄：Correction fluid used in ancient China）
天方夜谭 (noun)：虚妄荒诞的言论。（《天方夜谭》 is the previous translation of One Thousand and One Nights《一千零一夜》. Used for unfounded speech like a mythology / fairy tale）


Unbiased language
I personally use 乱说 rather than 胡说 or 瞎说.

胡 means foreign, e.g. 胡椒 black pepper (which is not origin in China). Although 胡 has the meaning of 乱 and beard/moustache in dictionary, I still think 胡说 is a stereotype on foreign citizens. Does foreigner's speech imply nonsense?
瞎 means is offensive way to say blind. 失明 and 视觉障碍 are inclusive language. I don't think 瞎说 is appropriate.