Significance of hour ruler

If hour ruler and Asc do not mesh well, does it make chart unreliable? Indicate negative answer? How important is the hour ruler?

This depends on how much emphasis you put on the considerations before judgment. I know some astrologers consider them more heavily than others and will see one and refuse to judge a chart. Others are more allowing, and still others usually have one or two pet considerations that their experience has shown them to be more of a red flag than others.

Personally, the hour ruler and Saturn in the Tenth for irrelevant questions are my two pet considerations.

I've found that if the ascendant and hour lord don't match, it tends to be an unimportant question. Either the matter they're inquiring about is A) none of the querent's business, B) not really what they want to know, or C) not serious enough for a horary.

So far it's served me well.

I myself do not use the hour ruler as a criterion (in this I follow the pre-Bonatti Islamic-era practitioners, as well as jyotish prasna authors)
However, give due consideration to the insightful post by K.N. Senshi, above!