How to Interpret 認不真 in 須認真. 若認不真. 便都成了假的?
「認真」is a common two characters compound word. It means 'serious' (adj.) 
Since it is an adjective, we can add the negative function word 「不」(not ) before it, and form an negative phrase  「不認真」(not serious)

However, 「認」on it's own can be the verb 'identify' or ' 'recognize' as in 「認人」(identify a person)，「認路」(recognize the way);  while 「真」on it's own can be the adjective 'true' or 'accurate' ; or the adverb 'truly' or 'accurately'

As a simple grammatical rule, an adverb can modify a verb.
Which mean 「認真」 can be treated as a [verb+ adverb] structure instead of a compound that we are familiar with. 

In the case of 「認不真」，「不」being a negative function word that modifies the adverb 「真」make it clear that the term we are looking at, is in fact [verb+ 不 + adverb] structure (認+不+真).

If 「不」 is placed before 「認真」, that would make it an [不 + adjective] structure (不+認真).


「不認真」means 'not serious'
「認不真」means 'cannot identify accurately' or 'not identify accurately'


As I mentioned before, 「認真」is a very common 'word' , to avoid confusion, it is better use 「認不清」 instead of 「認不真」. 

I believe if the phrase in question was 「認不真確」instead of the shortened 「認不真」, you would not be so confused. 

Since the common word 「認真」is widely used, putting 認 and 真 in a [verb + adverb] structure would certainly cause confusion. It is not recommended. 


  須認真.若認不真. 便都成了假的.


In this context 須認真 means " Need to identify accurately. 


  " Need to identify accurately. If not identify accurately, then everything will become (be treated as) fake"


I would suggest phrasing it as 「須認(得)真(確), 若認不真(確),  便都成了假的」 to make it more clear.