Low hardness at weldment and HAZ 1

Low hardness in fired tubes is not uncommon, the firing process anneals the tube and if its a welded in application the heat affected zone will be annealed from the welding.

You have not specified the metallurgy of the tubes, nor the hardness data. Also, design/operating temperature will help in making a rough analysis. A more accurate analysis would require thorough examination, including microstructures.

Does the low hardness cause a problem?

The tube material is 5Cr-0.5Mo steel. In my understanding, less than 120 HB should not be acceptable. I think about decarburization....Can anyone advise me about some references to study about its microstructure?

I did not see any detrimental effect in past operation. This is the first time that I check hardness at such location.

Quite possible that you've measured hardness of the surface, wich is decarburised. What is the indentation depth? If you have possibilty to destruct tobe - measure hardness in cross section. If you havent this possibilty - measure hardness after deeper grinding of tube surface.
The other case is overheating or burning of this steel. If this is so - thermal heating wont restore mechanical properties.
To find out the reason I recomend you to make microstructure testing.