Can a seller force me to take on unwanted liabilities as part of a share deal?

Not exactly "force," but in a share purchase there's no mechanism to cherry-pick which liabilities come along the way there is in an asset purchase. Because you're buying the corporation itself, its liabilities — the ones you like and the ones you don't — are part of what you're buying by definition; there's no schedule of "assumed liabilities" to negotiate down the way there is with assets.

What you can negotiate instead is protection against those liabilities, not their exclusion. Representations and warranties about the corporation's condition, indemnities that make the seller responsible if something turns out to be worse than represented, price adjustments, and a holdback or escrow to secure post-closing claims are all standard tools. If a particular liability is well understood and significant enough, it's also possible to deal with it specifically — through a targeted indemnity, an escrow tied just to that item, or requiring it be settled before closing.

If a specific liability is significant enough that you genuinely don't want it, that's often a sign the deal might work better as an asset purchase instead — a business lawyer can help you weigh which structure actually fits what you're trying to avoid.