Is it currently safe to travel through Sri Lanka?

The demonstrations and curfews you're referring to appear to be relatively recent, and western governments vary in their official travel advice concerning them. In the absence of someone "on the ground" stopping by and describing the situation, however, they're probably the best advice we can get. The general advice seems to be "exercise additional caution, but travel isn't necessarily unsafe." Given that Western governments tend to be highly cautious in these travel advisories, this is somewhat encouraging. If it were me, I would probably still avoid Kandy district to be on the safe side.

The United States government has not issued an official travel advisory concerning Sri Lanka. However, the local embassy issued some recommendations on March 6, 2018:

The Sri Lankan government declared an island-wide State of Emergency and curfews have been imposed in some regions due to communal unrest. Local authorities are authorized to declare local curfews. Further incidents are possible over the next few days.

Actions to Take:

• Avoid the areas of unrest.

• Exercise caution if unexpectedly in the vicinity of large gatherings or protests.

• Monitor local media for updates

• Keep a low profile.

The UK government says much the same thing (March 12, 2018):

A countrywide State of Emergency has been in force since 6 March 2018, following a number of violent incidents in Ampara and the Kandy area. Additional security personnel have been deployed in some areas, and access to a number of social media platforms is restricted. Bandaranaike International Airport in Colombo is operating as normal and there are no reports of ongoing incidents in major tourist areas.

If you’re in Sri Lanka or due to travel, you’re advised to exercise caution, avoid protests and rallies, and follow the advice of the local authorities. In addition to our travel advice, you may wish to consult the Sri Lankan Tourism Development Authority website, which has issued regular updates on the impact on tourist travel.

The French government's advice (March 12, 2018) is much the same:

Des incidents intercommunautaires violents se sont produits dans la région de Kandy (Digana, Teldeniya, Pallekele, centre du pays). Les mesures de sécurité mises en place par les autorités sri-lankaises sont détaillées sur le site de l’autorité en charge du développement du tourisme à Sri Lanka (en anglais) : http://www.sltda.lk/emergency . Il est recommandé de se tenir à l’écart des rassemblements, de respecter les consignes des autorités locales et de se tenir informé de l’évolution de la situation.

Violent intercommmunity incidents have occurred in the Kandy region (Digana, Teldeniya, Pallekele, and the center of the country.) The security measures put in place by Sri Lankan authorities are described on the site of the Sri Lankan Tourism Development Authority. It is recommended to stay away from gatherings, respect the orders of local authorities, and keep informed of the evolution of the situation.

The Canadian government tells its citizens to "Exercise a high degree of caution in Sri Lanka" (March 7, 2018), which is a slightly stronger statement than their usual "Exercise normal security precautions" but does not rise to the level of formally discouraging travel to the area.

Increasing inter-communal and religious tensions have led to recent violence in the Ampara and Kandy districts. On March 6, 2018, the Sri Lankan Government declared a 7-day state of emergency throughout the country. Authorities may impose curfews and other measures in response to further incidents to ensure safety and security. Access to some social media networks has been restricted. Comply with security instructions of local authorities, avoid large gatherings and monitor local media for the latest developments.

Finally, the Sri Lankan Tourist Development Authority (linked in the French travel advice above) says that there have been no further violent incidents since March 7. However, this particular office might have an incentive to gloss over legitimate safety concerns, so I would take this depiction with a grain of salt. The best assessment is probably somewhere between the Western government consensus above and the Sri Lankan government's assessment below.

The Kandy district has returned to normalcy and no violent incident has been reported from the area in the last 48 hours.

Tourists can now visit Kandy without any inconvenience, and members of the travel and hospitality industries will facilitate travel plans in Kandy.

Intermittent curfews imposed by the Police purely as a precautionary measure have no impact on tourists. Tourists can use their foreign passports as passes in the event of a curfew in the Kandy district.