Can one travel to Israel if his passport indicates he's been to Arab nations?

You will have absolutely no problem entering Israel. Israelis couldn't care less which countries you visited before. But as many people indicated here Some Muslim countries deny entry to anyone who has Israeli stamp in their passport. Israelis are well aware of that. It is a standard procedure to get a blank piece of paper to be stamped and stapled to your passport. Once you leave Israel you just remove and throw away this paper. However, as far as I know it is not done automatically. You need to ask for it at the passport control. However, like I said it is a common request that is is always granted without any questions asked. Don't worry, come and visit Israel. It is magnificent, beautiful country. Enjoy your stay.

It's not a problem. You can contact your Israeli embassy with your personal particulars to make sure.

The only security limits are per person, if you've been donating to a known terrorist organization, or supported terrorism. Also security screening is done by study of microexpressions that give away if your covering something up. So as long as you answer the security quiz questions honestly, you'll be fine. (And that micro expression stuff really does work -- they're looking for if you're carrying a "present" someone else put into your luggage to go "boom." Stuff like that.) So if his business company contacts were particularly connected to something shady, there could be a problem, otherwise not. (There's database research done before you arrive - same as the U.S. does.)

If your husband may need to travel to Arab countries again, then he's best asking at Israeli passports to stamp on a separate paper from his passport. There's a form for it now.

"Israeli Customs and Immigration officers may take a dim view of travelers arriving from Arab countries, but you are unlikely to face anything worse than very time-consuming and repetitive but polite questioning. Depending on the situation, if you have stamps from other Arab countries in your passport, you should expect to be taken to one side (without any explanation) and eventually questioned. This can take anywhere from 10 minutes to several hours. The key thing to remember is this: if you have nothing to hide, then, other than the inconvenience of questioning, you should have nothing to be worried about."

Also;

"Visa Restrictions:

Due to the ongoing Israeli-Palestinian dispute, Afghanistan, Algeria, Iran, Iraq, Kuwait, Lebanon, Libya, Saudi Arabia, Somalia, Sudan, Syria, and Yemen block passports containing stamps or visas from Israel. You may also have difficulties getting into and/or be refused visas to other Islamic countries, such as Bangladesh, Brunei, Indonesia, Malaysia, Pakistan, etc. If you intend to visit any of these nations, ask immigration to stamp a blank page, rather than your passport, when entering. Note that those countries will also search for Jordanian/Egyptian exit stamps from land borders with Israel and will likewise prohibit your entry if they find one."

Yes it is no problem but if he ever has to go back to Oman or Saudi Arabia he will have problems with an Israeli stamp on his passport.

Reverse is definitely true i.e. if you travel israel, you cant enter saudi. But as far as i remember, you should not have a problem with this case