With respect to proteins, usually beta-mercaptethanol (BME) forms (irreversible) covalent bonds with cysteine (sulfur containing) amino acid side chains which prevents oxidation (formation of intra/inter protein bonds) and dithiothreitol (DTT) also prevents oxidation but via a redox reaction with itself and is benign with respect to protein folding/structure.... Whatever, the point is that RNAses which will stuff up your RNA extraction can be deactivated with these chemicals during RNA extraction, BME is a sure bet so I would go with that - prep in a fume hood/tissue culture hood, it pongs worse than DTT, people get annoyed with it these days so just make sure your disposal routes are contained, clean up any spills immediately - bleach can oxidise it effectively if you do have a spill...

With respect to proteins, usually beta-mercaptethanol (BME) forms (irreversible) covalent bonds with cysteine (sulfur containing) amino acid side chains which prevents oxidation (formation of intra/inter protein bonds) and dithiothreitol (DTT) also prevents oxidation but via a redox reaction with itself and is benign with respect to protein folding/structure.... Whatever, the point is that RNAses which will stuff up your RNA extraction can be deactivated with these chemicals during RNA extraction, BME is a sure bet so I would go with that - prep in a fume hood/tissue culture hood, it pongs worse than DTT, people get annoyed with it these days so just make sure your disposal routes are contained, clean up any spills immediately - bleach can oxidise it effectively if you do have a spill...

Article Replacing β-mercaptoethanol in RNA extractions

I found this article to be informative.

"Overall, we found DTT to be more effective than β-ME in deactivating RNases but that using β-ME is better than using no reducing agent. The beneficial effect of using β-ME rather than no reducing agent was previously noted when Qiagen’s automated QIAsymphony technology was used to extract RNA from white blood cells that was subsequently analyzed by qRT–PCR [5]. Our results concur but also show that DTT could have been used instead, probably more effectively. Not only can DTT be used at a lower concentration than β-ME, but it is also less toxic and pungent; oral LD50 values (rat) are 244 mg/kg for β-ME but 400 mg/kg for DTT, and environmental LC50 values (Daphnia magna in 48 h) are 1.52 mg/L for β-ME and 27 mg/L for DTT [8], [9]. DTT has disadvantages compared with β-ME in that it has a shorter half-life and is supplied as a powder rather than as a solution, so it must be either freshly made up before sample homogenization or stored as frozen aliquots. However, we believe that the functional, practical, and safety-related advantages that DTT offers compared with β-ME clearly outweigh its more complex preparation and storage requirements. We believe that the widespread use of β-ME in RNA extractions can now justifiably be questioned, and we urge manufacturers of spin column purification kits to actively promote the less toxic DTT alternative."

I've always used BME with success.

Mostly in our lab, we used B-ME,