Can an online degree through an accredited institution affect admissions into masters programs abroad?
If you are seeking a BS degree from a United States accredited university through an online program, and wish to enter a Masters program with another U.S. accredited university, it should not be an issue on its own merits.

However, research universities may take a second look at your application if the online-achieved BS degree is not from another research institution.
To ensure your acceptance to such a Masters program, you will want to achieve a higher grade point average than expected. It would also help if you publish any articles during you progress towards the BS.

Other non-research institutions in this scenario should not have an issue accepting you with your online-achieved BS degree, so long as you clearly demonstrate in your application you meet all their requirements for admission.

Now, even with that said, non-research universities may even accept you even if you have defficiency in required undergrad coursework. In this case, a little real-world job experience as little as 1 year can help assure them you can do the work.

In all cases, don't underestimate the application letter you submit. I would make sure it communicates you have a goal in your education and career after the Masters. And it should demonstrate you are capable to meet their requirements, and to succeed in their program. That is ultimately what they are looking for.